Logiweb aspects of lemma lessAddition in pyk

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The predefined "pyk" aspect

define pyk of lemma lessAddition 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 s unicode small s unicode capital a unicode small d unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma lessAddition as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital a unicode small d unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma lessAddition 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 not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer not0 metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma lessAddition 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 not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer lemma lessLeq modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar <= metavar var y end metavar cut lemma leqAddition 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 lemma lessNeq modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar = metavar var y end metavar cut lemma neqAddition modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar cut prop lemma join conjuncts modus ponens metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var z end metavar modus ponens not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar conclude not0 metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar end quote state proof state cache var c end expand end define