Logiweb aspects of lemma minusTimesMinus in pyk

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The predefined "pyk" aspect

define pyk of lemma minusTimesMinus 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 m unicode small i unicode small n unicode small u unicode small s unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital m unicode small i unicode small n unicode small u unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma minusTimesMinus as text unicode start of text unicode capital m unicode small i unicode small n unicode small u unicode small s unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital m unicode small i unicode small n unicode small u 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 minusTimesMinus as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed - metavar var x end metavar * - metavar var y end metavar = metavar var x end metavar * metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma minusTimesMinus 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 lemma doubleMinus conclude - - metavar var y end metavar = metavar var y end metavar cut lemma times(-1)Left conclude - 1 * - metavar var y end metavar = - - metavar var y end metavar cut lemma eqTransitivity modus ponens - 1 * - metavar var y end metavar = - - metavar var y end metavar modus ponens - - metavar var y end metavar = metavar var y end metavar conclude - 1 * - metavar var y end metavar = metavar var y end metavar cut lemma eqMultiplicationLeft modus ponens - 1 * - metavar var y end metavar = metavar var y end metavar conclude metavar var x end metavar * - 1 * - metavar var y end metavar = metavar var x end metavar * metavar var y end metavar cut lemma times(-1) conclude metavar var x end metavar * - 1 = - metavar var x end metavar cut lemma eqMultiplication modus ponens metavar var x end metavar * - 1 = - metavar var x end metavar conclude metavar var x end metavar * - 1 * - metavar var y end metavar = - metavar var x end metavar * - metavar var y end metavar cut axiom timesAssociativity conclude metavar var x end metavar * - 1 * - metavar var y end metavar = metavar var x end metavar * - 1 * - metavar var y end metavar cut lemma equality modus ponens metavar var x end metavar * - 1 * - metavar var y end metavar = - metavar var x end metavar * - metavar var y end metavar modus ponens metavar var x end metavar * - 1 * - metavar var y end metavar = metavar var x end metavar * - 1 * - metavar var y end metavar conclude - metavar var x end metavar * - metavar var y end metavar = metavar var x end metavar * - 1 * - metavar var y end metavar cut lemma eqTransitivity modus ponens - metavar var x end metavar * - metavar var y end metavar = metavar var x end metavar * - 1 * - metavar var y end metavar modus ponens metavar var x end metavar * - 1 * - metavar var y end metavar = metavar var x end metavar * metavar var y end metavar conclude - metavar var x end metavar * - metavar var y end metavar = metavar var x end metavar * metavar var y end metavar end quote state proof state cache var c end expand end define