Logiweb aspects of lemma leqMax1 in pyk

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The predefined "pyk" aspect

define pyk of lemma leqMax1 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 l unicode small e unicode small q unicode capital m unicode small a unicode small x unicode one unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma leqMax1 as text unicode start of text unicode capital m unicode small a unicode small x unicode capital l unicode small e unicode small q 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 leqMax1 as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma leqMax1 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 lemma fromMax(1) modus ponens 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 cut lemma eqSymmetry modus ponens 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 metavar var x end metavar = if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut lemma eqLeq modus ponens metavar var x end metavar = if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) conclude metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var y end metavar <= metavar var x end metavar infer lemma fromMax(2) modus ponens not0 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 y end metavar cut lemma eqSymmetry modus ponens 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 metavar var y end metavar = if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut lemma toLess modus ponens not0 metavar var y end metavar <= metavar var x end metavar conclude not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut lemma lessLeq modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar <= metavar var y end metavar cut lemma subLeqRight modus ponens metavar var y end metavar = if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) modus ponens metavar var x end metavar <= metavar var y end metavar conclude metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens 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 metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) conclude metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var y end metavar <= metavar var x end metavar infer metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) conclude not0 metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) cut prop lemma from negations modus ponens metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) modus ponens not0 metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) conclude metavar var x end metavar <= if( metavar var y end metavar <= metavar var x end metavar , metavar var x end metavar , metavar var y end metavar ) end quote state proof state cache var c end expand end define