Logiweb aspects of lemma plusAssociativity(R) in pyk

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The predefined "pyk" aspect

define pyk of lemma plusAssociativity(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 a unicode small s unicode small s unicode small o unicode small c unicode small i 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 plusAssociativity(R) as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode capital a unicode small s unicode small s unicode small o unicode small c unicode small i 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 plusAssociativity(R) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma plusAssociativity(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 all metavar var fz end metavar indeed lemma plusAssociativity(F) conclude metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar =f metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar cut lemma =f to sameF modus ponens metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar =f metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar conclude metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar sameF metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar cut lemma f2R(Plus) modus ponens metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar sameF metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar conclude R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) cut lemma plusR(Sym) conclude R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( var fx +f var fy ) cut lemma ==Transitivity modus ponens R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( var fx +f var fy ) modus ponens R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) conclude R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) end quote state proof state cache var c end expand end define