Logiweb aspects of lemma minusNegated in pyk

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The predefined "pyk" aspect

define pyk of lemma minusNegated 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 n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma minusNegated as text unicode start of text unicode capital m unicode small i unicode small n unicode small u unicode small s unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma minusNegated 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 y end metavar + - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma minusNegated 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 eqAddition modus ponens - - metavar var y end metavar = metavar var y end metavar conclude - - metavar var y end metavar + - metavar var x end metavar = metavar var y end metavar + - metavar var x end metavar cut lemma eqSymmetry modus ponens - - metavar var y end metavar + - metavar var x end metavar = metavar var y end metavar + - metavar var x end metavar conclude metavar var y end metavar + - metavar var x end metavar = - - metavar var y end metavar + - metavar var x end metavar cut lemma -x-y=-(x+y) conclude - - metavar var y end metavar + - metavar var x end metavar = - - metavar var y end metavar + metavar var x end metavar cut axiom plusCommutativity conclude - metavar var y end metavar + metavar var x end metavar = metavar var x end metavar + - metavar var y end metavar cut lemma eqNegated modus ponens - metavar var y end metavar + metavar var x end metavar = metavar var x end metavar + - metavar var y end metavar conclude - - metavar var y end metavar + metavar var x end metavar = - metavar var x end metavar + - metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var y end metavar + - metavar var x end metavar = - - metavar var y end metavar + - metavar var x end metavar modus ponens - - metavar var y end metavar + - metavar var x end metavar = - - metavar var y end metavar + metavar var x end metavar modus ponens - - metavar var y end metavar + metavar var x end metavar = - metavar var x end metavar + - metavar var y end metavar conclude metavar var y end metavar + - metavar var x end metavar = - metavar var x end metavar + - metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar + - metavar var x 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 y end metavar + - metavar var x end metavar end quote state proof state cache var c end expand end define