Logiweb aspects of lemma (1/3)x+(1/3)x=(2/3)x in pyk

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The predefined "pyk" aspect

define pyk of lemma (1/3)x+(1/3)x=(2/3)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 equal sign unicode left parenthesis unicode two unicode slash unicode three unicode right parenthesis 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=(2/3)x as text unicode start of text 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 left parenthesis unicode two unicode slash unicode three unicode right parenthesis unicode small x 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=(2/3)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 + 1 + 1 * metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma (1/3)x+(1/3)x=(2/3)x as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed lemma x+x=2*x conclude 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut axiom timesAssociativity conclude 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqSymmetry modus ponens 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar conclude 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqTransitivity modus ponens 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar modus ponens 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * 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 + 1 + 1 * metavar var x end metavar cut 1rule repetition modus ponens 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * 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 + 1 + 1 * metavar var x end metavar end quote state proof state cache var c end expand end define