Logiweb aspects of lemma x=x+y-y in pyk

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The predefined "pyk" aspect

define pyk of lemma x=x+y-y 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 equal sign unicode small x unicode plus sign unicode small y unicode hyphen unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma x=x+y-y as text unicode start of text unicode small x unicode equal sign unicode small x unicode plus sign unicode small y unicode hyphen unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

define proof of lemma x=x+y-y 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 lemma x=x+(y-y) conclude metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut axiom plusAssociativity conclude metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar modus ponens metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar conclude metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar end quote state proof state cache var c end expand end define