define pyk of lemma lessNegated 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 n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define
define tex of lemma lessNegated as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define
define statement of lemma lessNegated as system Q infer all metavar var x end metavar indeed all metavar var y 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 x end metavar imply not0 not0 - metavar var y end metavar = - metavar var x end metavar end define
define proof of lemma lessNegated 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 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 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 leqNegated modus ponens metavar var x end metavar <= metavar var y end metavar conclude - metavar var y end metavar <= - metavar var x end metavar cut lemma lessNeq 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 not0 metavar var x end metavar = metavar var y end metavar cut lemma neqNegated modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude not0 - metavar var x end metavar = - metavar var y end metavar cut lemma neqSymmetry modus ponens not0 - metavar var x end metavar = - metavar var y end metavar conclude not0 - metavar var y end metavar = - metavar var x end metavar cut lemma leqNeqLess modus ponens - metavar var y end metavar <= - metavar var x end metavar modus ponens not0 - metavar var y end metavar = - metavar var x end metavar conclude not0 - metavar var y end metavar <= - metavar var x end metavar imply not0 not0 - metavar var y end metavar = - metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,