Logiweb aspects of lemma -x*y=-(x*y) in pyk

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The predefined "pyk" aspect

define pyk of lemma -x*y=-(x*y) as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode hyphen unicode small x unicode asterisk unicode small y unicode equal sign unicode hyphen unicode left parenthesis unicode small x unicode asterisk unicode small y unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma -x*y=-(x*y) as text unicode start of text unicode hyphen unicode small x unicode asterisk unicode small y unicode equal sign unicode hyphen unicode left parenthesis unicode small x unicode asterisk unicode small y 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 -x*y=-(x*y) 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 -x*y=-(x*y) 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 times(-1)Left conclude - 1 * metavar var x end metavar = - metavar var x end metavar cut lemma eqMultiplication modus ponens - 1 * metavar var x end metavar = - metavar var x end metavar conclude - 1 * metavar var x end metavar * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar cut lemma eqSymmetry modus ponens - 1 * metavar var x end metavar * 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 = - 1 * metavar var x end metavar * metavar var y end metavar cut axiom timesAssociativity conclude - 1 * metavar var x end metavar * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar cut lemma times(-1)Left conclude - 1 * metavar var x end metavar * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar cut lemma eqTransitivity4 modus ponens - metavar var x end metavar * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar modus ponens - 1 * metavar var x end metavar * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar modus ponens - 1 * metavar var x end metavar * 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