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
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
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
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
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,