define pyk of lemma <<==AntisymmetryHelper(Q) as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode less than unicode less than unicode equal sign unicode equal sign unicode capital a unicode small n unicode small t unicode small i unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode left parenthesis unicode capital q unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma <<==AntisymmetryHelper(Q) as text unicode start of text unicode less than unicode less than unicode equal sign unicode equal sign unicode capital a unicode small n unicode small t unicode small i unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode left parenthesis unicode capital q unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma <<==AntisymmetryHelper(Q) 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 not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar + - metavar var z end metavar infer metavar var y end metavar <= metavar var x end metavar + - metavar var z end metavar infer metavar var a end metavar end define
define proof of lemma <<==AntisymmetryHelper(Q) 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 not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar + - metavar var z end metavar infer metavar var y end metavar <= metavar var x end metavar + - metavar var z end metavar infer lemma leqAddition modus ponens metavar var x end metavar <= metavar var y end metavar + - metavar var z end metavar conclude metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut axiom plusAssociativity conclude metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut axiom plusCommutativity conclude - metavar var z end metavar + metavar var z end metavar = metavar var z end metavar + - metavar var z end metavar cut lemma eqAdditionLeft modus ponens - metavar var z end metavar + metavar var z end metavar = metavar var z end metavar + - metavar var z end metavar conclude metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma x=x+(y-y) conclude metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar conclude metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar modus ponens metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar modus ponens metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar conclude metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar cut lemma subLeqRight modus ponens metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar modus ponens metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar conclude metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar cut lemma leqTransitivity modus ponens metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar modus ponens metavar var y end metavar <= metavar var x end metavar + - metavar var z end metavar conclude metavar var x end metavar + metavar var z end metavar <= metavar var x end metavar + - metavar var z end metavar cut lemma leqSubtractionLeft modus ponens metavar var x end metavar + metavar var z end metavar <= metavar var x end metavar + - metavar var z end metavar conclude metavar var z end metavar <= - metavar var z end metavar cut lemma toNotLess modus ponens metavar var z end metavar <= - metavar var z end metavar conclude not0 not0 - metavar var z end metavar <= metavar var z end metavar imply not0 not0 - metavar var z end metavar = metavar var z end metavar cut lemma negativeLessPositive modus ponens not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar conclude not0 - metavar var z end metavar <= metavar var z end metavar imply not0 not0 - metavar var z end metavar = metavar var z end metavar cut prop lemma from contradiction modus ponens not0 - metavar var z end metavar <= metavar var z end metavar imply not0 not0 - metavar var z end metavar = metavar var z end metavar modus ponens not0 not0 - metavar var z end metavar <= metavar var z end metavar imply not0 not0 - metavar var z end metavar = metavar var z end metavar conclude metavar var a end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,