Logiweb aspects of lemma leqPlus1 in pyk

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The predefined "pyk" aspect

define pyk of lemma leqPlus1 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 p unicode small l unicode small u unicode small s unicode one unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma leqPlus1 as text unicode start of text unicode capital l unicode small e unicode small q unicode plus sign unicode one unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma leqPlus1 as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 metavar var x end metavar <= metavar var y end metavar + 1 imply not0 not0 metavar var x end metavar = metavar var y end metavar + 1 end define

The user defined "the proof aspect" aspect

define proof of lemma leqPlus1 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 metavar var x end metavar <= metavar var y end metavar infer lemma 0<1 conclude not0 0 <= 1 imply not0 not0 0 = 1 cut lemma lessAdditionLeft modus ponens not0 0 <= 1 imply not0 not0 0 = 1 conclude not0 metavar var y end metavar + 0 <= metavar var y end metavar + 1 imply not0 not0 metavar var y end metavar + 0 = metavar var y end metavar + 1 cut axiom plus0 conclude metavar var y end metavar + 0 = metavar var y end metavar cut lemma subLessLeft modus ponens metavar var y end metavar + 0 = metavar var y end metavar modus ponens not0 metavar var y end metavar + 0 <= metavar var y end metavar + 1 imply not0 not0 metavar var y end metavar + 0 = metavar var y end metavar + 1 conclude not0 metavar var y end metavar <= metavar var y end metavar + 1 imply not0 not0 metavar var y end metavar = metavar var y end metavar + 1 cut lemma leqLessTransitivity modus ponens metavar var x end metavar <= metavar var y end metavar modus ponens not0 metavar var y end metavar <= metavar var y end metavar + 1 imply not0 not0 metavar var y end metavar = metavar var y end metavar + 1 conclude not0 metavar var x end metavar <= metavar var y end metavar + 1 imply not0 not0 metavar var x end metavar = metavar var y end metavar + 1 end quote state proof state cache var c end expand end define