define pyk of lemma lessTransitivity 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 r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define
define tex of lemma lessTransitivity as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define
define statement of lemma lessTransitivity as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 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 y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar end define
define proof of lemma lessTransitivity 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 all metavar var z end metavar indeed 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 y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer prop lemma first conjunct modus ponens not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar conclude 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 <= metavar var z 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,