Logiweb aspects of lemma switchTerms(x<=y-z) in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma switchTerms(x<=y-z) 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 s unicode small w unicode small i unicode small t unicode small c unicode small h unicode capital t unicode small e unicode small r unicode small m unicode small s unicode left parenthesis unicode small x unicode less than unicode equal sign unicode small y unicode hyphen unicode small z unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma switchTerms(x<=y-z) as text unicode start of text unicode capital s unicode small w unicode small i unicode small t unicode small c unicode small h unicode capital t unicode small e unicode small r unicode small m unicode small s unicode left parenthesis unicode small x unicode less than unicode equal sign unicode small y unicode hyphen unicode small z 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 switchTerms(x<=y-z) 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 z end metavar <= metavar var y end metavar + - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma switchTerms(x<=y-z) 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 negativeToLeft(Leq) 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 cut axiom plusCommutativity conclude metavar var x end metavar + metavar var z end metavar = metavar var z end metavar + metavar var x end metavar cut lemma subLeqLeft modus ponens metavar var x end metavar + metavar var z end metavar = metavar var z end metavar + metavar var x end metavar modus ponens metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar conclude metavar var z end metavar + metavar var x end metavar <= metavar var y end metavar cut lemma positiveToRight(Leq) modus ponens metavar var z end metavar + metavar var x end metavar <= metavar var y end metavar conclude metavar var z end metavar <= metavar var y end metavar + - metavar var x end metavar end quote state proof state cache var c end expand end define