Logiweb aspects of system Q in pyk

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The predefined "pyk" aspect

define pyk of system Q as text unicode start of text unicode small s unicode small y unicode small s unicode small t unicode small e unicode small m unicode space unicode capital q unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of system Q as text unicode start of text unicode capital s unicode small y unicode small s unicode small t unicode small e unicode small m unicode capital q unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of system Q as all metavar var m end metavar indeed upperBound( [ us ; metavar var m end metavar ] , setOfFxs ) rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var fx end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar = metavar var ry end metavar infer metavar var fx end metavar in0 metavar var rx end metavar infer metavar var fx end metavar in0 metavar var ry end metavar rule plus all metavar var m end metavar indeed upperBound( the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set , setOfReals ) infer [ xs ; metavar var m end metavar + 1 ] = [ xs ; metavar var m end metavar ] rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar in0 metavar var x end metavar infer metavar var b end metavar infer metavar var y end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar = metavar var y end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var s end metavar in0 zermelo pair metavar var x end metavar comma metavar var y end metavar end pair imply not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply not0 not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar in0 zermelo pair metavar var x end metavar comma metavar var y end metavar end pair rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var sy end metavar indeed metavar var m end metavar in0 N imply not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sy end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair in0 metavar var fx end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed metavar var n end metavar = 0 infer base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = 1/ 1 + 1 ^ metavar var m end metavar rule plus all metavar var sx end metavar indeed all metavar var fy end metavar indeed for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fx end metavar imply object var var s1 end var in0 metavar var fy end metavar infer for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fy end metavar imply object var var s1 end var in0 metavar var fx end metavar infer metavar var fx end metavar = metavar var fy end metavar rule plus all metavar var x end metavar indeed metavar var x end metavar + 0 = metavar var x end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar <= metavar var y end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar infer metavar var a end metavar infer metavar var b end metavar rule plus all metavar var m end metavar indeed not0 [ ysF ; metavar var m end metavar ] <= [ xs ; metavar var m end metavar ] + 1/ metavar var m end metavar imply not0 not0 [ ysF ; metavar var m end metavar ] = [ xs ; metavar var m end metavar ] + 1/ metavar var m end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar in0 Q infer metavar var y end metavar in0 Q infer metavar var x end metavar * metavar var y end metavar in0 Q rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var fx end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed metavar var x end metavar * 1 = metavar var x end metavar rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed not0 metavar var sx end metavar = metavar var sy end metavar imply metavar var sx end metavar = metavar var sz end metavar infer metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer metavar var b end metavar rule plus all metavar var fx end metavar indeed all metavar var sy end metavar indeed lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) endorse not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sy end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar rule plus all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar = metavar var ry end metavar infer metavar var ry end metavar = metavar var rx end metavar rule plus all metavar var m end metavar indeed all metavar var x end metavar indeed metavar var m end metavar = 0 infer metavar var x end metavar ^ metavar var m end metavar = 1 rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 0 <= metavar var z end metavar imply metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar rule plus all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed metavar var sx end metavar = metavar var sx1 end metavar infer metavar var sy end metavar = metavar var sy1 end metavar infer zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer metavar var b end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus leastUpperBound( metavar var fx end metavar , metavar var fys end metavar ) infer not0 upperBound( metavar var fx end metavar , metavar var fys end metavar ) imply not0 upperBound( metavar var fz end metavar , metavar var fys end metavar ) imply not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ var x ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var imply metavar var fx end metavar = metavar var fz end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fxs end metavar indeed metavar var fx end metavar in0 metavar var fxs end metavar imply not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ var x ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var imply metavar var fx end metavar = metavar var fy end metavar infer upperBound( metavar var fy end metavar , metavar var fxs end metavar ) rule plus all metavar var fx end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus not0 0 = 1 rule plus all metavar var m end metavar indeed Nat( metavar var m end metavar ) endorse 0 <= metavar var m end metavar rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed not0 for all objects metavar var sy end metavar indeed not0 not0 metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sy end metavar in0 metavar var sz end metavar infer metavar var sx end metavar in0 U( metavar var sz end metavar ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar zermelo is metavar var y end metavar imply for all objects object var var s end var indeed not0 object var var s end var in0 metavar var x end metavar imply object var var s end var in0 metavar var y end metavar imply not0 object var var s end var in0 metavar var y end metavar imply object var var s end var in0 metavar var x end metavar imply not0 for all objects object var var s end var indeed not0 object var var s end var in0 metavar var x end metavar imply object var var s end var in0 metavar var y end metavar imply not0 object var var s end var in0 metavar var y end metavar imply object var var s end var in0 metavar var x end metavar imply metavar var x end metavar zermelo is metavar var y end metavar rule plus all metavar var x end metavar indeed not0 not0 0 <= metavar var x end metavar imply not0 | metavar var x end metavar | = metavar var x end metavar imply not0 not0 0 <= metavar var x end metavar imply not0 | metavar var x end metavar | = - metavar var x end metavar rule plus all metavar var rx end metavar indeed all metavar var ry end metavar indeed all metavar var rz end metavar indeed metavar var rx end metavar = metavar var ry end metavar infer metavar var ry end metavar = metavar var rz end metavar infer metavar var rx end metavar = metavar var rz end metavar rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed metavar var m end metavar = 0 infer metavar var fx end metavar ^ metavar var m end metavar = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar + metavar var y end metavar = metavar var y end metavar + metavar var x end metavar rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] rule plus all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed meta-sub metavar var b end metavar is metavar var a end metavar where metavar var v1 end metavar is 0 end sub endorse meta-sub metavar var c end metavar is metavar var a end metavar where metavar var v1 end metavar is metavar var v1 end metavar + 1 end sub endorse metavar var b end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar imply metavar var c end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar rule plus all metavar var m end metavar indeed not0 upperBound( [ xs ; metavar var m end metavar ] , setOfFxs ) rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed metavar var sx end metavar = metavar var sy end metavar infer metavar var sx end metavar in0 metavar var sz end metavar infer metavar var sy end metavar in0 metavar var sz end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed metavar var n end metavar = 0 infer UStelescope( metavar var m end metavar , metavar var n end metavar ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar * metavar var y end metavar = metavar var y end metavar * metavar var x end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar in0 the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar rule plus all metavar var a end metavar indeed metavar var a end metavar infer metavar var a end metavar rule plus all metavar var m end metavar indeed lambda var c dot typeNat0( quote metavar var m end metavar end quote ) endorse metavar var m end metavar in0 N rule plus all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair in0 the set of ph in power power U( zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 metavar var sx1 end metavar imply not0 object var var op2 end var in0 metavar var sy1 end metavar imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set infer metavar var sy end metavar in0 metavar var sy1 end metavar rule plus all metavar var m end metavar indeed upperBound( the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set , setOfReals ) infer [ us ; metavar var m end metavar + 1 ] = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sx end metavar imply object var var s1 end var in0 metavar var sy end metavar infer metavar var sx end metavar in0 power metavar var sy end metavar end power rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed not0 metavar var s end metavar in0 power metavar var x end metavar end power imply for all objects object var var s end var indeed object var var s end var in0 metavar var s end metavar imply object var var s end var in0 metavar var x end metavar imply not0 for all objects object var var s end var indeed object var var s end var in0 metavar var s end metavar imply object var var s end var in0 metavar var x end metavar imply metavar var s end metavar in0 power metavar var x end metavar end power rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar = metavar var fy end metavar infer the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fx end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fy end metavar ; object var var m end var ] <= [ metavar var fz end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fz end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fz end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fx end metavar ; object var var m end var ] <= [ metavar var fz end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fz end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fz end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ var x ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fxs end metavar indeed upperBound( metavar var fy end metavar , metavar var fxs end metavar ) infer metavar var fx end metavar in0 metavar var fxs end metavar infer not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ var x ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var imply metavar var fx end metavar = metavar var fy end metavar rule plus all metavar var m end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fx end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var infer not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] <= [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - object var var ep end var rule plus [ us ; 0 ] = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed metavar var x end metavar <= metavar var x end metavar rule plus all metavar var s end metavar indeed not0 metavar var s end metavar in0 zermelo empty set rule plus all metavar var fx end metavar indeed not0 not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var imply for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ metavar var fx end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ metavar var fx end metavar ; object var var m end var ] | = object var var ep end var imply |f metavar var fx end metavar | = metavar var fx end metavar imply not0 not0 not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var imply for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ metavar var fx end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ metavar var fx end metavar ; object var var m end var ] | = object var var ep end var imply |f metavar var fx end metavar | = the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma - [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed not0 0 <= metavar var m end metavar imply not0 not0 0 = metavar var m end metavar infer metavar var fx end metavar ^ metavar var m end metavar = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] * [ var y ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] * [ var y ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed metavar var x end metavar + - metavar var x end metavar = 0 rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair imply not0 [ metavar var fx end metavar ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] = if( [ metavar var fx end metavar ; metavar var m end metavar ] = 0 , 0 , 1/ [ metavar var fx end metavar ; metavar var m end metavar ] ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar = metavar var z end metavar imply metavar var y end metavar = metavar var z end metavar rule plus all metavar var m end metavar indeed not0 [ xs ; metavar var m end metavar ] <= [ ysF ; metavar var m end metavar ] imply not0 not0 [ xs ; metavar var m end metavar ] = [ ysF ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar in0 Q infer metavar var y end metavar in0 Q infer metavar var x end metavar + metavar var y end metavar in0 Q rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed not0 0 <= metavar var n end metavar imply not0 not0 0 = metavar var n end metavar infer UStelescope( metavar var m end metavar , metavar var n end metavar ) = | [ us ; metavar var m end metavar + metavar var n end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + - 1 ) rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed not0 metavar var x end metavar = 0 imply metavar var x end metavar * 1/ metavar var x end metavar = 1 rule plus all metavar var x end metavar indeed not0 metavar var x end metavar = 0 imply metavar var x end metavar in0 Q imply 1/ metavar var x end metavar in0 Q rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed not0 metavar var b end metavar imply metavar var a end metavar infer not0 metavar var b end metavar imply not0 metavar var a end metavar infer metavar var b end metavar rule plus all metavar var x end metavar indeed lambda var c dot typeRational0( quote metavar var x end metavar end quote ) endorse metavar var x end metavar in0 Q rule plus all metavar var rx end metavar indeed metavar var rx end metavar = metavar var rx end metavar rule plus all metavar var m end metavar indeed not0 upperBound( the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set , setOfReals ) infer [ us ; metavar var m end metavar + 1 ] = [ us ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var z end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var p end metavar indeed all metavar var x end metavar indeed all metavar var z end metavar indeed metavar var p end metavar is placeholder-var and ph-sub metavar var b end metavar is metavar var a end metavar where metavar var p end metavar is metavar var z end metavar end sub endorse not0 metavar var z end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var z end metavar in0 metavar var x end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var z end metavar in0 metavar var x end metavar imply not0 metavar var b end metavar imply metavar var z end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer metavar var y end metavar in0 metavar var x end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fx end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] <= [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var m end metavar indeed all metavar var m1 end metavar indeed all metavar var n end metavar indeed metavar var m end metavar <= metavar var n end metavar infer not0 for all objects metavar var m1 end metavar indeed not0 metavar var m end metavar + metavar var m1 end metavar = metavar var n end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var fep end metavar indeed all metavar var fx end metavar indeed all metavar var fys end metavar indeed limit( metavar var fx end metavar , metavar var fys end metavar ) infer for all objects metavar var fep end metavar indeed not0 for all objects metavar var m end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var imply metavar var m end metavar <= metavar var n end metavar imply not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ |f the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma - [ var x ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set | ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma - [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma - [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar * metavar var y end metavar + metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * metavar var z end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed Nat( metavar var m end metavar ) endorse Nat( metavar var n end metavar ) endorse not0 metavar var m end metavar <= metavar var n end metavar + 1 imply not0 not0 metavar var m end metavar = metavar var n end metavar + 1 infer metavar var m end metavar <= metavar var n end metavar rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair infer not0 metavar var sx end metavar = metavar var sy end metavar imply metavar var sx end metavar = metavar var sz end metavar rule plus all metavar var x end metavar indeed metavar var x end metavar in0 Q imply - metavar var x end metavar in0 Q rule plus all metavar var x end metavar indeed all metavar var t end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed exist-sub0 quote metavar var a end metavar end quote is quote metavar var b end metavar end quote where quote metavar var x end metavar end quote is quote metavar var t end metavar end quote end sub endorse metavar var a end metavar infer metavar var b end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar imply not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var y end metavar rule plus all metavar var m end metavar indeed all metavar var x end metavar indeed not0 0 <= metavar var m end metavar imply not0 not0 0 = metavar var m end metavar infer metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + - 1 rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var y end metavar + metavar var z end metavar rule plus all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sx end metavar = metavar var sy end metavar infer zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair rule plus all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var v1 end metavar imply metavar var n end metavar <= metavar var v2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = metavar var ep end metavar rule plus all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed meta-sub metavar var a end metavar is metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed metavar var b end metavar imply metavar var a end metavar rule plus all metavar var fx end metavar indeed all metavar var fz end metavar indeed all metavar var fys end metavar indeed upperBound( metavar var fx end metavar , metavar var fys end metavar ) infer upperBound( metavar var fz end metavar , metavar var fys end metavar ) imply not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ var x ; object var var m end var ] <= [ var y ; object var var m end var ] + - object var var ep end var imply metavar var fx end metavar = metavar var fz end metavar infer leastUpperBound( metavar var fx end metavar , metavar var fys end metavar ) rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed not0 0 <= metavar var n end metavar imply not0 not0 0 = metavar var n end metavar infer base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + - 1 ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar * metavar var y end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar * metavar var z end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var infer the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar rule plus all metavar var x end metavar indeed all metavar var a end metavar indeed metavar var a end metavar infer for all objects metavar var x end metavar indeed metavar var a end metavar rule plus all metavar var m end metavar indeed all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 for all objects metavar var m end metavar indeed not0 not0 1/ metavar var m end metavar <= metavar var x end metavar imply not0 not0 1/ metavar var m end metavar = metavar var x end metavar rule plus all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair in0 the set of ph in power power U( zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 metavar var sx1 end metavar imply not0 object var var op2 end var in0 metavar var sy1 end metavar imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set infer metavar var sx end metavar in0 metavar var sx1 end metavar rule plus all metavar var m end metavar indeed not0 upperBound( the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set , setOfReals ) infer [ xs ; metavar var m end metavar + 1 ] = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 1/ [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair imply not0 [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] + [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = 0 imply not0 placeholder-var var f end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma 0 end pair end pair end set ; metavar var m end metavar ] * [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var d end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ var x ; metavar var m end metavar ] + [ var y ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer not0 metavar var y end metavar in0 metavar var x end metavar imply not0 metavar var b end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var z end metavar imply metavar var x end metavar <= metavar var z end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed not0 metavar var s end metavar in0 union metavar var x end metavar end union imply not0 metavar var s end metavar in0 existential var var j end var imply not0 existential var var j end var in0 metavar var x end metavar imply not0 not0 metavar var s end metavar in0 existential var var j end var imply not0 existential var var j end var in0 metavar var x end metavar imply metavar var s end metavar in0 union metavar var x end metavar end union rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects metavar var m end metavar indeed not0 placeholder-var var e end var = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus all metavar var fx end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar = metavar var ry end metavar infer metavar var fx end metavar in0 metavar var ry end metavar infer metavar var fx end metavar in0 metavar var rx end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fx end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fy end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var imply the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set rule plus not0 the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 0 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 placeholder-var var f end var imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 placeholder-var var f end var imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma 1 end pair end pair end set ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set end define