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

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The predefined "pyk" aspect

define pyk of lemma -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 hyphen 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 hyphen 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 -x+(1/3)x=-(2/3)x as text unicode start of text unicode hyphen 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 hyphen 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 -x+(1/3)x=-(2/3)x as system Q infer all metavar var x end metavar indeed - 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 -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 (2/3)x+(1/3)x=x conclude 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar cut lemma positiveToRight(Eq) modus ponens 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar conclude 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqNegated modus ponens 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar conclude - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = - metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma minusNegated conclude - 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 cut axiom plusCommutativity conclude 1/ 1 + 1 + 1 * metavar var x end metavar + - metavar var x end metavar = - metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqTransitivity4 modus ponens - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = - metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar modus ponens - 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 modus ponens 1/ 1 + 1 + 1 * metavar var x end metavar + - metavar var x end metavar = - metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar conclude - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar = - metavar var x end metavar + 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 = - metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar conclude - 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