Logiweb aspects of lemma eqNegated in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma eqNegated 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 e unicode small q 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 eqNegated as text unicode start of text unicode capital e unicode small q 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 eqNegated 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 infer - metavar var x end metavar = - metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma eqNegated 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 metavar var x end metavar = metavar var y end metavar infer axiom negative conclude metavar var x end metavar + - metavar var x end metavar = 0 cut axiom negative conclude metavar var y end metavar + - metavar var y end metavar = 0 cut lemma eqSymmetry modus ponens metavar var y end metavar + - metavar var y end metavar = 0 conclude 0 = metavar var y end metavar + - metavar var y end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar + - metavar var x end metavar = 0 modus ponens 0 = metavar var y end metavar + - metavar var y end metavar conclude metavar var x end metavar + - metavar var x end metavar = metavar var y end metavar + - metavar var y end metavar cut lemma subtractEquationsLeft modus ponens metavar var x end metavar + - metavar var x end metavar = metavar var y end metavar + - metavar var y end metavar modus ponens metavar var x end metavar = metavar var y end metavar conclude - metavar var x end metavar = - metavar var y end metavar end quote state proof state cache var c end expand end define