Logiweb aspects of lemma equivalence class is subset in pyk

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The predefined "pyk" aspect

define pyk of lemma equivalence class is subset 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 e unicode small q unicode small u unicode small i unicode small v unicode small a unicode small l unicode small e unicode small n unicode small c unicode small e unicode space unicode small c unicode small l unicode small a unicode small s unicode small s unicode space unicode small i unicode small s unicode space unicode small s unicode small u unicode small b unicode small s unicode small e unicode small t unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma equivalence class is subset as text unicode start of text unicode capital e unicode small q unicode capital c unicode small l unicode small a unicode small s unicode small s unicode capital i unicode small s unicode capital s unicode small u unicode small b unicode small s unicode small e unicode small t unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma equivalence class is subset as system zf infer all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var big set end metavar indeed metavar var s end metavar zermelo in 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 metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set imply metavar var s end metavar zermelo in metavar var big set end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma equivalence class is subset 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 s end metavar indeed all metavar var x end metavar indeed all metavar var big set end metavar indeed metavar var s end metavar zermelo in 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 metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set infer lemma separation2formula modus ponens metavar var s end metavar zermelo in 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 metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set conclude not0 metavar var s end metavar zermelo in metavar var big set end metavar imply not0 zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar cut prop lemma first conjunct modus ponens not0 metavar var s end metavar zermelo in metavar var big set end metavar imply not0 zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar conclude metavar var s end metavar zermelo in metavar var big set end metavar cut all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var x 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 s end metavar indeed all metavar var x end metavar indeed all metavar var big set end metavar indeed metavar var s end metavar zermelo in 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 metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set infer metavar var s end metavar zermelo in metavar var big set end metavar conclude metavar var s end metavar zermelo in 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 metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set imply metavar var s end metavar zermelo in metavar var big set end metavar end quote state proof state cache var c end expand end define