Logiweb aspects of pred lemma addExist(Simple) in pyk

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The predefined "pyk" aspect

define pyk of pred lemma addExist(Simple) 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 left parenthesis unicode capital s unicode small i unicode small m unicode small p unicode small l unicode small e unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of pred lemma addExist(Simple) 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 left parenthesis unicode capital s unicode small i unicode small m unicode small p unicode small l unicode small e 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 addExist(Simple) as system Q infer 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 metavar var a end metavar imply metavar var b end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var b end metavar end define

The user defined "the proof aspect" aspect

define proof of pred lemma addExist(Simple) 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 v2 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar infer prop lemma auto imply conclude metavar var a end metavar imply metavar var a end metavar cut pred lemma addExist at metavar var v2 end metavar modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens metavar var a end metavar imply metavar var a end metavar conclude not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var b end metavar end quote state proof state cache var c end expand end define