Logiweb aspects of lemma (1/3)x+(1/3)x+(1/3)x=x in pyk

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The predefined "pyk" aspect

define pyk of lemma (1/3)x+(1/3)x+(1/3)x=x 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 one unicode slash unicode three unicode right parenthesis unicode small x unicode plus sign unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode plus sign unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode equal sign unicode small x unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma (1/3)x+(1/3)x+(1/3)x=x as text unicode start of text unicode capital t unicode small h unicode small r unicode small e unicode small e unicode capital t unicode small h unicode small i unicode small r unicode small d unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma (1/3)x+(1/3)x+(1/3)x=x as system Q infer all metavar var x end metavar indeed 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma (1/3)x+(1/3)x+(1/3)x=x as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed lemma 0<3 conclude not0 0 <= 1 + 1 + 1 imply not0 not0 0 = 1 + 1 + 1 cut lemma positiveNonzero modus ponens not0 0 <= 1 + 1 + 1 imply not0 not0 0 = 1 + 1 + 1 conclude not0 1 + 1 + 1 = 0 cut lemma x+x+x=3*x conclude 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut axiom timesAssociativity conclude 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqSymmetry modus ponens 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar conclude 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma reciprocal modus ponens not0 1 + 1 + 1 = 0 conclude 1 + 1 + 1 * 1/ 1 + 1 + 1 = 1 cut lemma eqMultiplication modus ponens 1 + 1 + 1 * 1/ 1 + 1 + 1 = 1 conclude 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 * metavar var x end metavar cut lemma times1Left conclude 1 * metavar var x end metavar = metavar var x end metavar cut lemma eqTransitivity5 modus ponens 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar modus ponens 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar modus ponens 1 + 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 * metavar var x end metavar modus ponens 1 * metavar var x end metavar = metavar var x end metavar conclude 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define