Logiweb aspects of lemma multiplyEquations in pyk

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The predefined "pyk" aspect

define pyk of lemma multiplyEquations 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 m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small y unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma multiplyEquations as text unicode start of text unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small y unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma multiplyEquations as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed all metavar var u end metavar indeed metavar var x end metavar = metavar var y end metavar infer metavar var z end metavar = metavar var u end metavar infer metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var u end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma multiplyEquations 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 all metavar var z end metavar indeed all metavar var u end metavar indeed metavar var x end metavar = metavar var y end metavar infer metavar var z end metavar = metavar var u end metavar infer lemma eqMultiplication modus ponens metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar cut lemma eqMultiplicationLeft modus ponens metavar var z end metavar = metavar var u end metavar conclude metavar var y end metavar * metavar var z end metavar = metavar var y end metavar * metavar var u end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar modus ponens metavar var y end metavar * metavar var z end metavar = metavar var y end metavar * metavar var u end metavar conclude metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var u end metavar end quote state proof state cache var c end expand end define