Logiweb aspects of lemma leqMultiplicationLeft in pyk

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The predefined "pyk" aspect

define pyk of lemma leqMultiplicationLeft 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 l unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode capital l unicode small e unicode small f unicode small t unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma leqMultiplicationLeft as text unicode start of text unicode capital l unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode capital l unicode small e unicode small f unicode small t unicode space unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma leqMultiplicationLeft 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 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 x end metavar <= metavar var z end metavar * metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma leqMultiplicationLeft 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 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y 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 axiom timesCommutativity conclude metavar var x end metavar * metavar var z end metavar = metavar var z end metavar * metavar var x end metavar cut lemma subLeqLeft modus ponens metavar var x end metavar * metavar var z end metavar = metavar var z end metavar * metavar var x end metavar modus ponens metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar conclude metavar var z end metavar * metavar var x end metavar <= metavar var y end metavar * metavar var z end metavar cut axiom timesCommutativity conclude metavar var y end metavar * metavar var z end metavar = metavar var z end metavar * metavar var y end metavar cut lemma subLeqRight modus ponens metavar var y end metavar * metavar var z end metavar = metavar var z end metavar * metavar var y end metavar modus ponens metavar var z end metavar * metavar var x end metavar <= metavar var y end metavar * metavar var z end metavar conclude metavar var z end metavar * metavar var x end metavar <= metavar var z end metavar * metavar var y end metavar end quote state proof state cache var c end expand end define