Logiweb aspects of axiom numericalF in pyk

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The predefined "pyk" aspect

define pyk of axiom numericalF as text unicode start of text unicode small a unicode small x unicode small i unicode small o unicode small m unicode space unicode small n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode capital f unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of axiom numericalF as text unicode start of text unicode capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode capital f unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of axiom numericalF as system Q infer 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 end define

The user defined "the proof aspect" aspect

define proof of axiom numericalF as rule tactic end define