define pyk of lemma 0<2 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 two unicode end of text end unicode text end text end define
define tex of lemma 0<2 as text unicode start of text unicode zero unicode less than unicode two unicode end of text end unicode text end text end define
define statement of lemma 0<2 as system Q infer not0 0 <= 1 + 1 imply not0 not0 0 = 1 + 1 end define
define proof of lemma 0<2 as lambda var c dot lambda var x dot proof expand quote system Q infer lemma 0<1 conclude not0 0 <= 1 imply not0 not0 0 = 1 cut lemma lessAddition modus ponens not0 0 <= 1 imply not0 not0 0 = 1 conclude not0 0 + 1 <= 1 + 1 imply not0 not0 0 + 1 = 1 + 1 cut lemma plus0Left conclude 0 + 1 = 1 cut lemma subLessLeft modus ponens 0 + 1 = 1 modus ponens not0 0 + 1 <= 1 + 1 imply not0 not0 0 + 1 = 1 + 1 conclude not0 1 <= 1 + 1 imply not0 not0 1 = 1 + 1 cut lemma lessTransitivity modus ponens not0 0 <= 1 imply not0 not0 0 = 1 modus ponens not0 1 <= 1 + 1 imply not0 not0 1 = 1 + 1 conclude not0 0 <= 1 + 1 imply not0 not0 0 = 1 + 1 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,