define pyk of lemma (-1)*(-1)+(-1)*1=0 as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode asterisk unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode plus sign unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode asterisk unicode one unicode equal sign unicode zero unicode end of text end unicode text end text end define
define tex of lemma (-1)*(-1)+(-1)*1=0 as text unicode start of text unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode asterisk unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode plus sign unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode asterisk unicode one unicode equal sign unicode zero unicode end of text end unicode text end text end define
define statement of lemma (-1)*(-1)+(-1)*1=0 as system Q infer - 1 * - 1 + - 1 * 1 = 0 end define
define proof of lemma (-1)*(-1)+(-1)*1=0 as lambda var c dot lambda var x dot proof expand quote system Q infer lemma distributionOut conclude - 1 * - 1 + - 1 * 1 = - 1 * - 1 + 1 cut axiom negative conclude 1 + - 1 = 0 cut axiom plusCommutativity conclude - 1 + 1 = 1 + - 1 cut lemma eqTransitivity modus ponens - 1 + 1 = 1 + - 1 modus ponens 1 + - 1 = 0 conclude - 1 + 1 = 0 cut lemma eqMultiplicationLeft modus ponens - 1 + 1 = 0 conclude - 1 * - 1 + 1 = - 1 * 0 cut lemma x*0=0 conclude - 1 * 0 = 0 cut lemma eqTransitivity4 modus ponens - 1 * - 1 + - 1 * 1 = - 1 * - 1 + 1 modus ponens - 1 * - 1 + 1 = - 1 * 0 modus ponens - 1 * 0 = 0 conclude - 1 * - 1 + - 1 * 1 = 0 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,