Logiweb aspects of lemma induction in pyk

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The predefined "pyk" aspect

define pyk of lemma induction 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 i unicode small n unicode small d unicode small u unicode small c unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma induction as text unicode start of text unicode capital i unicode small n unicode small d unicode small u unicode small c unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma induction as system Q infer 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 infer metavar var a end metavar imply metavar var c end metavar infer metavar var a end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma induction as lambda var c dot lambda var x dot proof expand quote system Q infer 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 infer metavar var a end metavar imply metavar var c end metavar infer 1rule gen modus ponens metavar var a end metavar imply metavar var c end metavar conclude for all objects metavar var v1 end metavar indeed metavar var a end metavar imply metavar var c end metavar cut axiom induction modus probans meta-sub metavar var b end metavar is metavar var a end metavar where metavar var v1 end metavar is 0 end sub modus probans 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 conclude 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 cut prop lemma mp2 modus ponens 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 modus ponens metavar var b end metavar modus ponens for all objects metavar var v1 end metavar indeed metavar var a end metavar imply metavar var c end metavar conclude for all objects metavar var v1 end metavar indeed metavar var a end metavar cut lemma a4 at metavar var v1 end metavar modus ponens for all objects metavar var v1 end metavar indeed metavar var a end metavar conclude metavar var a end metavar end quote state proof state cache var c end expand end define