Logiweb aspects of lemma fromOrderedPair(twoLevels) in pyk

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The predefined "pyk" aspect

define pyk of lemma fromOrderedPair(twoLevels) 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 f unicode small r unicode small o unicode small m unicode capital o unicode small r unicode small d unicode small e unicode small r unicode small e unicode small d unicode capital p unicode small a unicode small i unicode small r unicode left parenthesis unicode small t unicode small w unicode small o unicode capital l unicode small e unicode small v unicode small e unicode small l unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromOrderedPair(twoLevels) as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital o unicode small r unicode small d unicode small e unicode small r unicode small e unicode small d unicode capital p unicode small a unicode small i unicode small r unicode left parenthesis unicode capital t unicode small w unicode small o unicode capital l unicode small e unicode small v unicode small e unicode small l unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromOrderedPair(twoLevels) as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sx end metavar in0 metavar var sy end metavar infer metavar var sy end metavar in0 zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair end pair infer not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromOrderedPair(twoLevels) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sx end metavar in0 metavar var sy end metavar infer metavar var sy end metavar in0 zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair end pair infer 1rule repetition modus ponens metavar var sy end metavar in0 zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair end pair conclude metavar var sy end metavar in0 zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair end pair cut lemma pair2formula modus ponens metavar var sy end metavar in0 zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair end pair conclude not0 metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair imply metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair cut all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair infer metavar var sx end metavar in0 metavar var sy end metavar infer lemma set equality nec condition(1) modus ponens metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair modus ponens metavar var sx end metavar in0 metavar var sy end metavar conclude metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair cut lemma fromSingleton modus ponens metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair conclude metavar var sx end metavar = metavar var sz end metavar cut prop lemma weaken or second modus ponens metavar var sx end metavar = metavar var sz end metavar conclude not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar cut all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair infer metavar var sx end metavar in0 metavar var sy end metavar infer lemma set equality nec condition(1) modus ponens metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair modus ponens metavar var sx end metavar in0 metavar var sy end metavar conclude metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair cut lemma pair2formula modus ponens metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair conclude not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar cut 1rule deduction modus ponens all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair infer metavar var sx end metavar in0 metavar var sy end metavar infer not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar conclude metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair imply metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar cut 1rule deduction modus ponens all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair infer metavar var sx end metavar in0 metavar var sy end metavar infer not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar conclude metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair imply metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar cut prop lemma from disjuncts modus ponens not0 metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair imply metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair modus ponens metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair imply metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar modus ponens metavar var sy end metavar = zermelo pair metavar var sz end metavar comma metavar var su end metavar end pair imply metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar conclude metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar cut 1rule mp modus ponens metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar modus ponens metavar var sx end metavar in0 metavar var sy end metavar conclude not0 metavar var sx end metavar = metavar var sz end metavar imply metavar var sx end metavar = metavar var su end metavar end quote state proof state cache var c end expand end define