Logiweb aspects of lemma fromMax(1) in pyk

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The predefined "pyk" aspect

define pyk of lemma fromMax(1) 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 m unicode small a unicode small x unicode left parenthesis unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromMax(1) as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital m unicode small a unicode small x unicode left parenthesis unicode one 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 fromMax(1) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar <= metavar var x end metavar infer if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromMax(1) 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 y end metavar indeed metavar var y end metavar <= metavar var x end metavar infer axiom max conclude not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar imply not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var y end metavar cut prop lemma add double neg modus ponens metavar var y end metavar <= metavar var x end metavar conclude not0 not0 metavar var y end metavar <= metavar var x end metavar cut prop lemma to negated and(1) modus ponens not0 not0 metavar var y end metavar <= metavar var x end metavar conclude not0 not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var y end metavar cut prop lemma negate second disjunct modus ponens not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar imply not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var y end metavar modus ponens not0 not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var y end metavar conclude not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar cut prop lemma second conjunct modus ponens not0 metavar var y end metavar <= metavar var x end metavar imply not0 if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar conclude if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) = metavar var x end metavar end quote state proof state cache var c end expand end define