Logiweb aspects of lemma x+x+x=3*x in pyk

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The predefined "pyk" aspect

define pyk of lemma x+x+x=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 small x unicode plus sign unicode small x unicode plus sign unicode small x unicode equal sign unicode three unicode asterisk unicode small x unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma x+x+x=3*x as text unicode start of text unicode capital t unicode small h unicode small r unicode small e unicode small e unicode capital w unicode small h unicode small o unicode small l unicode small e 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 x+x+x=3*x as system Q infer all metavar var x end metavar indeed metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 + 1 * metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma x+x+x=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 metavar var x end metavar + metavar var x end metavar = 1 + 1 * metavar var x end metavar cut lemma times1Left conclude 1 * metavar var x end metavar = metavar var x end metavar cut lemma eqSymmetry modus ponens 1 * metavar var x end metavar = metavar var x end metavar conclude metavar var x end metavar = 1 * metavar var x end metavar cut lemma addEquations modus ponens metavar var x end metavar + metavar var x end metavar = 1 + 1 * metavar var x end metavar modus ponens metavar var x end metavar = 1 * metavar var x end metavar conclude metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 * metavar var x end metavar + 1 * metavar var x end metavar cut lemma distributionOutLeft conclude 1 + 1 * metavar var x end metavar + 1 * metavar var x end metavar = metavar var x end metavar * 1 + 1 + 1 cut axiom timesCommutativity conclude metavar var x end metavar * 1 + 1 + 1 = 1 + 1 + 1 * metavar var x end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 * metavar var x end metavar + 1 * metavar var x end metavar modus ponens 1 + 1 * metavar var x end metavar + 1 * metavar var x end metavar = metavar var x end metavar * 1 + 1 + 1 modus ponens metavar var x end metavar * 1 + 1 + 1 = 1 + 1 + 1 * metavar var x end metavar conclude metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 + 1 * metavar var x end metavar cut 1rule repetition modus ponens metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 + 1 * metavar var x end metavar conclude metavar var x end metavar + metavar var x end metavar + metavar var x end metavar = 1 + 1 + 1 * metavar var x end metavar end quote state proof state cache var c end expand end define