Logiweb aspects of lemma x*0=0 in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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