Logiweb aspects of lemma plusCommutativity(R) in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma plusCommutativity(R) 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 p unicode small l unicode small u unicode small s unicode capital c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma plusCommutativity(R) as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode capital c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode left parenthesis unicode capital r 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 plusCommutativity(R) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed R( var fx +f var fy ) == R( var fx +f var fy ) end define

The user defined "the proof aspect" aspect

define proof of lemma plusCommutativity(R) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed lemma plusCommutativity(F) conclude metavar var fx end metavar +f metavar var fy end metavar =f metavar var fy end metavar +f metavar var fx end metavar cut lemma =f to sameF modus ponens metavar var fx end metavar +f metavar var fy end metavar =f metavar var fy end metavar +f metavar var fx end metavar conclude metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fy end metavar +f metavar var fx end metavar cut lemma f2R(Plus) modus ponens metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fy end metavar +f metavar var fx end metavar conclude R( var fx +f var fy ) == R( metavar var fy end metavar +f metavar var fx end metavar ) cut lemma plusR(Sym) conclude R( metavar var fy end metavar +f metavar var fx end metavar ) == R( var fx +f var fy ) cut lemma ==Transitivity modus ponens R( var fx +f var fy ) == R( metavar var fy end metavar +f metavar var fx end metavar ) modus ponens R( metavar var fy end metavar +f metavar var fx end metavar ) == R( var fx +f var fy ) conclude R( var fx +f var fy ) == R( var fx +f var fy ) end quote state proof state cache var c end expand end define