Logiweb aspects of pred lemma intro exist helper in pyk

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The predefined "pyk" aspect

define pyk of pred lemma intro exist helper as text unicode start of text unicode small p unicode small r unicode small e unicode small d unicode space 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 t unicode small r unicode small o unicode space unicode small e unicode small x unicode small i unicode small s unicode small t unicode space unicode small h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of pred lemma intro exist helper as text unicode start of text unicode capital i unicode small n unicode small t unicode small r unicode small o unicode capital e unicode small x unicode small i unicode small s unicode small t unicode left parenthesis unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of pred lemma intro exist helper as system Q infer all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed meta-sub not0 metavar var a end metavar is not0 metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed not0 metavar var b end metavar imply not0 metavar var a end metavar end define

The user defined "the proof aspect" aspect

define proof of pred lemma intro exist helper as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed meta-sub not0 metavar var a end metavar is not0 metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed not0 metavar var b end metavar infer lemma a4 at metavar var x end metavar modus probans meta-sub not0 metavar var a end metavar is not0 metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub modus ponens for all objects metavar var v1 end metavar indeed not0 metavar var b end metavar conclude not0 metavar var a end metavar cut all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed meta-sub not0 metavar var a end metavar is not0 metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed not0 metavar var b end metavar infer not0 metavar var a end metavar conclude meta-sub not0 metavar var a end metavar is not0 metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed not0 metavar var b end metavar imply not0 metavar var a end metavar end quote state proof state cache var c end expand end define