Logiweb aspects of lemma negativeNegated in pyk

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The predefined "pyk" aspect

define pyk of lemma negativeNegated 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 n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma negativeNegated as text unicode start of text unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma negativeNegated as system Q infer all metavar var x end metavar indeed not0 metavar var x end metavar <= 0 imply not0 not0 metavar var x end metavar = 0 infer not0 0 <= - metavar var x end metavar imply not0 not0 0 = - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma negativeNegated as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed not0 metavar var x end metavar <= 0 imply not0 not0 metavar var x end metavar = 0 infer lemma lessNegated modus ponens not0 metavar var x end metavar <= 0 imply not0 not0 metavar var x end metavar = 0 conclude not0 - 0 <= - metavar var x end metavar imply not0 not0 - 0 = - metavar var x end metavar cut lemma -0=0 conclude - 0 = 0 cut lemma subLessLeft modus ponens - 0 = 0 modus ponens not0 - 0 <= - metavar var x end metavar imply not0 not0 - 0 = - metavar var x end metavar conclude not0 0 <= - metavar var x end metavar imply not0 not0 0 = - metavar var x end metavar end quote state proof state cache var c end expand end define