Logiweb aspects of lemma subtractEquations in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma subtractEquations 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 u unicode small b unicode small t unicode small r unicode small a unicode small c unicode small t 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma subtractEquations as text unicode start of text unicode capital s unicode small u unicode small b unicode small t unicode small r unicode small a unicode small c unicode small t 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma subtractEquations 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 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar infer metavar var z end metavar = metavar var u end metavar infer metavar var x end metavar = metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma subtractEquations 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 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar infer metavar var z end metavar = metavar var u end metavar infer lemma eqAddition modus ponens metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var u end metavar conclude metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar cut lemma plus0Left conclude 0 + metavar var z end metavar = metavar var z end metavar cut lemma eqTransitivity modus ponens 0 + metavar var z end metavar = metavar var z end metavar modus ponens metavar var z end metavar = metavar var u end metavar conclude 0 + metavar var z end metavar = metavar var u end metavar cut lemma positiveToRight(Eq) modus ponens 0 + metavar var z end metavar = metavar var u end metavar conclude 0 = metavar var u end metavar + - metavar var z end metavar cut lemma eqSymmetry modus ponens 0 = metavar var u end metavar + - metavar var z end metavar conclude metavar var u end metavar + - metavar var z end metavar = 0 cut lemma eqAdditionLeft modus ponens metavar var u end metavar + - metavar var z end metavar = 0 conclude metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar + 0 cut axiom plusAssociativity conclude metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar cut axiom plus0 conclude metavar var y end metavar + 0 = metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar modus ponens metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar + 0 modus ponens metavar var y end metavar + 0 = metavar var y end metavar conclude metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar cut lemma x=x+y-y conclude metavar var x end metavar = metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar = metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar modus ponens metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar modus ponens metavar var y end metavar + metavar var u end metavar + - metavar var z end metavar = metavar var y end metavar conclude metavar var x end metavar = metavar var y end metavar end quote state proof state cache var c end expand end define