Logiweb aspects of lemma times(-1) in pyk

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The predefined "pyk" aspect

define pyk of lemma times(-1) 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 t unicode small i unicode small m unicode small e unicode small s unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma times(-1) as text unicode start of text unicode capital t unicode small i unicode small m unicode small e unicode small s unicode left parenthesis unicode hyphen unicode one 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 times(-1) as system Q infer all metavar var x end metavar indeed metavar var x end metavar * - 1 = - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma times(-1) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed axiom negative conclude 1 + - 1 = 0 cut axiom plusCommutativity conclude - 1 + 1 = 1 + - 1 cut lemma eqTransitivity modus ponens - 1 + 1 = 1 + - 1 modus ponens 1 + - 1 = 0 conclude - 1 + 1 = 0 cut lemma eqMultiplicationLeft modus ponens - 1 + 1 = 0 conclude metavar var x end metavar * - 1 + 1 = metavar var x end metavar * 0 cut lemma x*0=0 conclude metavar var x end metavar * 0 = 0 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 + 1 = metavar var x end metavar * 0 modus ponens metavar var x end metavar * 0 = 0 conclude metavar var x end metavar * - 1 + 1 = 0 cut axiom distribution conclude metavar var x end metavar * - 1 + 1 = metavar var x end metavar * - 1 + metavar var x end metavar * 1 cut lemma eqSymmetry modus ponens metavar var x end metavar * - 1 + 1 = metavar var x end metavar * - 1 + metavar var x end metavar * 1 conclude metavar var x end metavar * - 1 + metavar var x end metavar * 1 = metavar var x end metavar * - 1 + 1 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 + metavar var x end metavar * 1 = metavar var x end metavar * - 1 + 1 modus ponens metavar var x end metavar * - 1 + 1 = 0 conclude metavar var x end metavar * - 1 + metavar var x end metavar * 1 = 0 cut lemma positiveToRight(Eq) modus ponens metavar var x end metavar * - 1 + metavar var x end metavar * 1 = 0 conclude metavar var x end metavar * - 1 = 0 + - metavar var x end metavar * 1 cut lemma plus0Left conclude 0 + - metavar var x end metavar * 1 = - metavar var x end metavar * 1 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 = 0 + - metavar var x end metavar * 1 modus ponens 0 + - metavar var x end metavar * 1 = - metavar var x end metavar * 1 conclude metavar var x end metavar * - 1 = - metavar var x end metavar * 1 cut axiom times1 conclude metavar var x end metavar * 1 = metavar var x end metavar cut lemma eqNegated modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude - metavar var x end metavar * 1 = - metavar var x end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 = - metavar var x end metavar * 1 modus ponens - metavar var x end metavar * 1 = - metavar var x end metavar conclude metavar var x end metavar * - 1 = - metavar var x end metavar end quote state proof state cache var c end expand end define