Logiweb aspects of lemma lessThanMax in pyk

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The predefined "pyk" aspect

define pyk of lemma lessThanMax 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 s unicode small s unicode capital t unicode small h unicode small a unicode small n unicode capital m unicode small a unicode small x unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma lessThanMax as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital t unicode small h unicode small a unicode small n unicode capital m unicode small a unicode small x unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma lessThanMax as system Q infer all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar infer not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma lessThanMax as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer metavar var a end metavar infer 1rule mp modus ponens metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar modus ponens metavar var a 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 leqMax1 conclude metavar var y end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut lemma lessLeqTransitivity 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 modus ponens metavar var y end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) conclude not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar infer not0 metavar var a end metavar infer 1rule mp modus ponens not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar modus ponens not0 metavar var a end metavar conclude not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar cut lemma leqMax2 conclude metavar var z end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut lemma lessLeqTransitivity modus ponens not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar modus ponens metavar var z end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) conclude not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer metavar var a end metavar infer not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) conclude metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar imply metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar infer not0 metavar var a end metavar infer not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) conclude not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar imply not0 metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar infer 1rule mp modus ponens metavar var a end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar imply metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) modus ponens metavar var a end metavar imply 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 a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut 1rule mp modus ponens not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar imply not0 metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) modus ponens not0 metavar var a end metavar imply not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar conclude not0 metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) cut prop lemma from negations modus ponens metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) modus ponens not0 metavar var a end metavar imply not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) conclude not0 metavar var x end metavar <= if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) imply not0 not0 metavar var x end metavar = if( metavar var z end metavar <= metavar var y end metavar , metavar var y end metavar , metavar var z end metavar ) end quote state proof state cache var c end expand end define