define pyk of lemma 0<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 zero unicode less than unicode one unicode end of text end unicode text end text end define
define tex of lemma 0<1 as text unicode start of text unicode zero unicode less than unicode one unicode end of text end unicode text end text end define
define statement of lemma 0<1 as system Q infer not0 0 <= 1 imply not0 not0 0 = 1 end define
define proof of lemma 0<1 as lambda var c dot lambda var x dot proof expand quote system Q infer axiom leqTotality conclude not0 0 <= 1 imply 1 <= 0 cut prop lemma auto imply conclude 0 <= 1 imply 0 <= 1 cut lemma 0<1Helper conclude 1 <= 0 imply 0 <= 1 cut prop lemma from disjuncts modus ponens not0 0 <= 1 imply 1 <= 0 modus ponens 0 <= 1 imply 0 <= 1 modus ponens 1 <= 0 imply 0 <= 1 conclude 0 <= 1 cut axiom 0not1 conclude not0 0 = 1 cut prop lemma join conjuncts modus ponens 0 <= 1 modus ponens not0 0 = 1 conclude not0 0 <= 1 imply not0 not0 0 = 1 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,