Logiweb aspects of lemma x*0+x=x in pyk

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The predefined "pyk" aspect

define pyk of lemma x*0+x=x 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 plus sign unicode small x unicode equal sign unicode small x unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma x*0+x=x as text unicode start of text unicode small x unicode asterisk unicode zero unicode plus sign unicode small x unicode equal sign unicode small x unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma x*0+x=x as system Q infer all metavar var x end metavar indeed metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma x*0+x=x as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed axiom times1 conclude metavar var x end metavar * 1 = metavar var x end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude metavar var x end metavar = metavar var x end metavar * 1 cut lemma eqAdditionLeft modus ponens metavar var x end metavar = metavar var x end metavar * 1 conclude metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar * 1 cut axiom distribution conclude metavar var x end metavar * 0 + 1 = metavar var x end metavar * 0 + metavar var x end metavar * 1 cut lemma eqSymmetry modus ponens metavar var x end metavar * 0 + 1 = metavar var x end metavar * 0 + metavar var x end metavar * 1 conclude metavar var x end metavar * 0 + metavar var x end metavar * 1 = metavar var x end metavar * 0 + 1 cut lemma plus0Left conclude 0 + 1 = 1 cut lemma eqMultiplicationLeft modus ponens 0 + 1 = 1 conclude metavar var x end metavar * 0 + 1 = metavar var x end metavar * 1 cut lemma eqTransitivity5 modus ponens metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar * 1 modus ponens metavar var x end metavar * 0 + metavar var x end metavar * 1 = metavar var x end metavar * 0 + 1 modus ponens metavar var x end metavar * 0 + 1 = metavar var x end metavar * 1 modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define