Logiweb aspects of lemma addEquations(Less) in pyk

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The predefined "pyk" aspect

define pyk of lemma addEquations(Less) 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 a unicode small d unicode small d unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma addEquations(Less) as text unicode start of text unicode capital a unicode small d unicode small d unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s 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 addEquations(Less) 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 all metavar var u 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 z end metavar <= metavar var u end metavar imply not0 not0 metavar var z end metavar = metavar var u end metavar infer not0 metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var u end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma addEquations(Less) 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 all metavar var u 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 z end metavar <= metavar var u end metavar imply not0 not0 metavar var z end metavar = metavar var u end metavar infer lemma lessAddition 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 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 cut lemma lessAdditionLeft modus ponens not0 metavar var z end metavar <= metavar var u end metavar imply not0 not0 metavar var z end metavar = metavar var u end metavar conclude not0 metavar var y end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var u end metavar imply not0 not0 metavar var y end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar cut lemma lessTransitivity modus ponens 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 modus ponens not0 metavar var y end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var u end metavar imply not0 not0 metavar var y end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar conclude not0 metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var u end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar end quote state proof state cache var c end expand end define