Logiweb aspects of lemma all disjoint-imply in pyk

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The predefined "pyk" aspect

define pyk of lemma all disjoint-imply as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small a unicode small l unicode small l unicode space unicode small d unicode small i unicode small s unicode small j unicode small o unicode small i unicode small n unicode small t unicode hyphen unicode small i unicode small m unicode small p unicode small l unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma all disjoint-imply as text unicode start of text unicode capital a unicode small l unicode small l unicode capital d unicode small i unicode small s unicode small j unicode small o unicode small i unicode small n unicode small t unicode capital i unicode small m unicode small p unicode small l unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma all disjoint-imply as system zf infer all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var big set end metavar end quote endorse not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply metavar var x end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set imply metavar var y end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set imply not0 metavar var x end metavar zermelo is metavar var y end metavar imply the set of ph in union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end pair end union such that not0 placeholder-var var c end var zermelo in metavar var x end metavar imply not0 placeholder-var var c end var zermelo in metavar var y end metavar end set zermelo is zermelo empty set end define

The user defined "the proof aspect" aspect

define proof of lemma all disjoint-imply as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar infer metavar var x end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set infer metavar var y end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set infer not0 metavar var x end metavar zermelo is metavar var y end metavar infer cheating axiom all disjoint modus ponens not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar modus ponens metavar var x end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set modus ponens metavar var y end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set modus ponens not0 metavar var x end metavar zermelo is metavar var y end metavar conclude the set of ph in union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end pair end union such that not0 placeholder-var var c end var zermelo in metavar var x end metavar imply not0 placeholder-var var c end var zermelo in metavar var y end metavar end set zermelo is zermelo empty set cut all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed 1rule deduction modus ponens all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar infer metavar var x end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set infer metavar var y end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set infer not0 metavar var x end metavar zermelo is metavar var y end metavar infer the set of ph in union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end pair end union such that not0 placeholder-var var c end var zermelo in metavar var x end metavar imply not0 placeholder-var var c end var zermelo in metavar var y end metavar end set zermelo is zermelo empty set conclude quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var big set end metavar end quote endorse not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply metavar var x end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set imply metavar var y end metavar zermelo in the set of ph in power metavar var big set end metavar end power such that not0 existential var var t end var zermelo in metavar var big set end metavar imply not0 the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma existential var var t end var end pair end pair zermelo in metavar var r end metavar end set zermelo is placeholder-var var b end var end set imply not0 metavar var x end metavar zermelo is metavar var y end metavar imply the set of ph in union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end pair end union such that not0 placeholder-var var c end var zermelo in metavar var x end metavar imply not0 placeholder-var var c end var zermelo in metavar var y end metavar end set zermelo is zermelo empty set end quote state proof state cache var c end expand end define