Logiweb aspects of lemma negativeToLeft(Leq) in pyk

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The predefined "pyk" aspect

define pyk of lemma negativeToLeft(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 l unicode small e unicode small f 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 predefined "tex" aspect

define tex of lemma negativeToLeft(Leq) as text unicode start of text 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 l unicode small e unicode small f 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 negativeToLeft(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 negativeToLeft(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 z end metavar <= metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma x=x+y-y conclude metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma three2threeTerms conclude metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma eqTransitivity modus ponens metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar modus ponens metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar conclude metavar var y end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar 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 x end metavar + metavar var z end metavar <= metavar var y end metavar + - metavar var z end metavar + metavar var z 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