Logiweb aspects of lemma multiplyEquations(Leq) in pyk

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The predefined "pyk" aspect

define pyk of lemma multiplyEquations(Leq) 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 left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma multiplyEquations(Leq) 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 left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma multiplyEquations(Leq) 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 0 <= metavar var x end metavar infer 0 <= metavar var z end metavar infer 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(Leq) 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 0 <= metavar var x end metavar infer 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar infer metavar var z end metavar <= metavar var u end metavar infer lemma leqMultiplication modus ponens 0 <= metavar var z end metavar 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 leqTransitivity modus ponens 0 <= metavar var x end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude 0 <= metavar var y end metavar cut lemma leqMultiplicationLeft modus ponens 0 <= metavar var y end metavar 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 leqTransitivity 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