Logiweb aspects of lemma distributionOut(Minus) in pyk

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The predefined "pyk" aspect

define pyk of lemma distributionOut(Minus) 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 d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode capital o unicode small u unicode small t unicode left parenthesis unicode capital m unicode small i unicode small n unicode small u unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma distributionOut(Minus) as text unicode start of text unicode capital d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode capital o unicode small u unicode small t unicode left parenthesis unicode capital m unicode small i unicode small n unicode small u unicode small s 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 distributionOut(Minus) 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 metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma distributionOut(Minus) 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 lemma times(-1)Left conclude - 1 * metavar var x end metavar * metavar var z end metavar = - metavar var x end metavar * metavar var z end metavar cut lemma eqSymmetry modus ponens - 1 * metavar var x end metavar * metavar var z end metavar = - metavar var x end metavar * metavar var z end metavar conclude - metavar var x end metavar * metavar var z end metavar = - 1 * metavar var x end metavar * metavar var z end metavar cut axiom timesCommutativity conclude - 1 * metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * - 1 cut axiom timesAssociativity conclude metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * metavar var z end metavar * - 1 cut lemma times(-1) conclude metavar var z end metavar * - 1 = - metavar var z end metavar cut lemma eqMultiplicationLeft modus ponens metavar var z end metavar * - 1 = - metavar var z end metavar conclude metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * - metavar var z end metavar cut lemma eqTransitivity5 modus ponens - metavar var x end metavar * metavar var z end metavar = - 1 * metavar var x end metavar * metavar var z end metavar modus ponens - 1 * metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * - 1 modus ponens metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * metavar var z end metavar * - 1 modus ponens metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * - metavar var z end metavar conclude - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * - metavar var z end metavar cut lemma eqAdditionLeft modus ponens - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * - metavar var z end metavar conclude metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar cut lemma distributionOut conclude metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar modus ponens metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar conclude metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar end quote state proof state cache var c end expand end define