define pyk of lemma x*0=0 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 x unicode asterisk unicode zero unicode equal sign unicode zero unicode end of text end unicode text end text end define
define tex of lemma x*0=0 as text unicode start of text unicode small x unicode asterisk unicode zero unicode equal sign unicode zero unicode end of text end unicode text end text end define
define statement of lemma x*0=0 as system Q infer all metavar var x end metavar indeed metavar var x end metavar * 0 = 0 end define
define proof of lemma x*0=0 as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed lemma x=x+(y-y) conclude metavar var x end metavar * 0 = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar cut axiom plusAssociativity conclude metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar conclude metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar cut lemma x*0+x=x conclude metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar cut lemma eqAddition modus ponens metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar conclude metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar + - metavar var x end metavar cut axiom negative conclude metavar var x end metavar + - metavar var x end metavar = 0 cut lemma eqTransitivity5 modus ponens metavar var x end metavar * 0 = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar modus ponens metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar modus ponens metavar var x end metavar * 0 + metavar var x end metavar + - metavar var x end metavar = metavar var x end metavar + - metavar var x end metavar modus ponens metavar var x end metavar + - metavar var x end metavar = 0 conclude metavar var x end metavar * 0 = 0 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,