Logiweb aspects of lemma sameReciprocal in pyk

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The predefined "pyk" aspect

define pyk of lemma sameReciprocal 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 s unicode small a unicode small m unicode small e unicode capital r unicode small e unicode small c unicode small i unicode small p unicode small r unicode small o unicode small c unicode small a unicode small l unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameReciprocal as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital r unicode small e unicode small c unicode small i unicode small p unicode small r unicode small o unicode small c unicode small a unicode small l unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameReciprocal as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar = 0 infer metavar var x end metavar = metavar var y end metavar infer 1/ metavar var x end metavar = 1/ metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma sameReciprocal as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar = 0 infer metavar var x end metavar = metavar var y end metavar infer lemma times1Left conclude 1 * metavar var x end metavar = metavar var x end metavar cut lemma eqTransitivity modus ponens 1 * metavar var x end metavar = metavar var x end metavar modus ponens metavar var x end metavar = metavar var y end metavar conclude 1 * metavar var x end metavar = metavar var y end metavar cut lemma nonreciprocalToRight(Eq) modus ponens not0 metavar var x end metavar = 0 modus ponens 1 * metavar var x end metavar = metavar var y end metavar conclude 1 = metavar var y end metavar * 1/ metavar var x end metavar cut axiom timesCommutativity conclude metavar var y end metavar * 1/ metavar var x end metavar = 1/ metavar var x end metavar * metavar var y end metavar cut lemma eqTransitivity modus ponens 1 = metavar var y end metavar * 1/ metavar var x end metavar modus ponens metavar var y end metavar * 1/ metavar var x end metavar = 1/ metavar var x end metavar * metavar var y end metavar conclude 1 = 1/ metavar var x end metavar * metavar var y end metavar cut lemma nonreciprocalToLeft(Eq)(1 term) modus ponens 1 = 1/ metavar var x end metavar * metavar var y end metavar conclude 1/ metavar var y end metavar = 1/ metavar var x end metavar cut lemma eqSymmetry modus ponens 1/ metavar var y end metavar = 1/ metavar var x end metavar conclude 1/ metavar var x end metavar = 1/ metavar var y end metavar end quote state proof state cache var c end expand end define