Logiweb aspects of pred lemma addExist in pyk

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The predefined "pyk" aspect

define pyk of pred lemma addExist 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 a unicode small d unicode small d unicode capital e unicode small x unicode small i unicode small s unicode small t unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of pred lemma addExist as text unicode start of text unicode capital a unicode small d unicode small d unicode capital e unicode small x unicode small i unicode small s unicode small t unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of pred lemma addExist as system Q infer all metavar var y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar infer metavar var c end metavar imply metavar var a end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar end define

The user defined "the proof aspect" aspect

define proof of pred lemma addExist as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar infer metavar var c end metavar imply metavar var a end metavar infer pred lemma addExist helper2 modus probans meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub conclude metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar cut prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens metavar var c end metavar imply metavar var a end metavar conclude not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar end quote state proof state cache var c end expand end define