Logiweb aspects of lemma |x-x|=0 in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma |x-x|=0 as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode vertical line unicode small x unicode hyphen unicode small x unicode vertical line unicode equal sign unicode zero unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma |x-x|=0 as text unicode start of text unicode vertical line unicode small x unicode hyphen unicode small x unicode vertical line unicode equal sign unicode zero unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma |x-x|=0 as system Q infer all metavar var x end metavar indeed | metavar var x end metavar + - metavar var x end metavar | = 0 end define

The user defined "the proof aspect" aspect

define proof of lemma |x-x|=0 as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed lemma eqReflexivity conclude metavar var x end metavar = metavar var x end metavar cut lemma positiveToLeft(Eq)(1 term) modus ponens metavar var x end metavar = metavar var x end metavar conclude metavar var x end metavar + - metavar var x end metavar = 0 cut lemma sameNumerical modus ponens metavar var x end metavar + - metavar var x end metavar = 0 conclude | metavar var x end metavar + - metavar var x end metavar | = | 0 | cut lemma |0|=0 conclude | 0 | = 0 cut lemma eqTransitivity modus ponens | metavar var x end metavar + - metavar var x end metavar | = | 0 | modus ponens | 0 | = 0 conclude | metavar var x end metavar + - metavar var x end metavar | = 0 end quote state proof state cache var c end expand end define