Logiweb aspects of lemma leqNegated in pyk

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The predefined "pyk" aspect

define pyk of lemma leqNegated 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 l 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 leqNegated as text unicode start of text unicode capital l 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 user defined "the statement aspect" aspect

define statement of lemma leqNegated 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 y end metavar <= - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma leqNegated 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 lemma leqAddition modus ponens metavar var x 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 x end metavar cut axiom negative conclude metavar var x end metavar + - metavar var x end metavar = 0 cut lemma subLeqLeft modus ponens metavar var x end metavar + - metavar var x end metavar = 0 modus ponens metavar var x end metavar + - metavar var x end metavar <= metavar var y end metavar + - metavar var x end metavar conclude 0 <= 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 subLeqRight modus ponens metavar var y end metavar + - metavar var x end metavar = - metavar var x end metavar + metavar var y end metavar modus ponens 0 <= metavar var y end metavar + - metavar var x end metavar conclude 0 <= - metavar var x end metavar + metavar var y end metavar cut lemma leqAddition modus ponens 0 <= - metavar var x end metavar + metavar var y end metavar conclude 0 + - metavar var y end metavar <= - metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma plus0Left conclude 0 + - metavar var y end metavar = - metavar var y end metavar cut lemma x=x+y-y conclude - metavar var x end metavar = - metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma eqSymmetry modus ponens - metavar var x end metavar = - metavar var x end metavar + metavar var y 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 cut lemma subLeqLeft modus ponens 0 + - metavar var y end metavar = - metavar var y end metavar modus ponens 0 + - metavar var y end metavar <= - metavar var x end metavar + 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 y end metavar cut lemma subLeqRight modus ponens - metavar var x end metavar + metavar var y 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 y end metavar conclude - metavar var y end metavar <= - metavar var x end metavar end quote state proof state cache var c end expand end define