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 hyphen unicode small y unicode equal sign unicode hyphen unicode left parenthesis unicode small x unicode plus sign unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma -x-y=-(x+y) as text unicode start of text unicode hyphen unicode small x unicode hyphen unicode small y unicode equal sign unicode hyphen unicode left parenthesis unicode small x unicode plus sign unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
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
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 times(-1)Left conclude - 1 * metavar var y end metavar = - metavar var y end metavar cut lemma addEquations modus ponens - 1 * metavar var x end metavar = - metavar var x end metavar modus ponens - 1 * metavar var y end metavar = - metavar var y end metavar conclude - 1 * metavar var x end metavar + - 1 * 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 + - 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 = - 1 * metavar var x end metavar + - 1 * metavar var y end metavar cut lemma distributionOut conclude - 1 * metavar var x end metavar + - 1 * 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 + - 1 * metavar var y end metavar modus ponens - 1 * metavar var x end metavar + - 1 * 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
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,