Logiweb aspects of lemma negativeToRight(Leq) in pyk

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The predefined "pyk" aspect

define pyk of lemma negativeToRight(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 n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital r unicode small i unicode small g unicode small h unicode small t 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 negativeToRight(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 metavar var x end metavar + - metavar var y end metavar <= metavar var z end metavar infer 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 negativeToRight(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 metavar var x end metavar + - metavar var y end metavar <= metavar var z end metavar infer lemma leqAddition modus ponens metavar var x end metavar + - metavar var y end metavar <= metavar var z end metavar conclude metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar <= metavar var z end metavar + metavar var y end metavar cut 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 lemma three2threeTerms 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 cut lemma eqSymmetry modus ponens metavar var x 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 cut lemma subLeqLeft modus ponens metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar = metavar var x end metavar modus ponens metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar <= metavar var z end metavar + metavar var y end metavar conclude 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