Logiweb aspects of lemma positiveInverted in pyk

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The predefined "pyk" aspect

define pyk of lemma positiveInverted 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 p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital i unicode small n unicode small v unicode small e unicode small r unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma positiveInverted as text unicode start of text unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital i unicode small n unicode small v unicode small e unicode small r unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma positiveInverted as system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 0 <= 1/ metavar var x end metavar imply not0 not0 0 = 1/ metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma positiveInverted as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer prop lemma first conjunct modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude 0 <= metavar var x end metavar cut prop lemma second conjunct modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 0 = metavar var x end metavar cut lemma neqSymmetry modus ponens not0 0 = metavar var x end metavar conclude not0 metavar var x end metavar = 0 cut lemma 0<1 conclude not0 0 <= 1 imply not0 not0 0 = 1 cut lemma x*0=0 conclude metavar var x end metavar * 0 = 0 cut lemma x*y=zBackwards modus ponens metavar var x end metavar * 0 = 0 conclude 0 = 0 * metavar var x end metavar cut lemma subLessLeft modus ponens 0 = 0 * metavar var x end metavar modus ponens not0 0 <= 1 imply not0 not0 0 = 1 conclude not0 0 * metavar var x end metavar <= 1 imply not0 not0 0 * metavar var x end metavar = 1 cut lemma reciprocal modus ponens not0 metavar var x end metavar = 0 conclude metavar var x end metavar * 1/ metavar var x end metavar = 1 cut lemma x*y=zBackwards modus ponens metavar var x end metavar * 1/ metavar var x end metavar = 1 conclude 1 = 1/ metavar var x end metavar * metavar var x end metavar cut lemma subLessRight modus ponens 1 = 1/ metavar var x end metavar * metavar var x end metavar modus ponens not0 0 * metavar var x end metavar <= 1 imply not0 not0 0 * metavar var x end metavar = 1 conclude not0 0 * metavar var x end metavar <= 1/ metavar var x end metavar * metavar var x end metavar imply not0 not0 0 * metavar var x end metavar = 1/ metavar var x end metavar * metavar var x end metavar cut lemma lessDivision modus ponens 0 <= metavar var x end metavar modus ponens not0 0 * metavar var x end metavar <= 1/ metavar var x end metavar * metavar var x end metavar imply not0 not0 0 * metavar var x end metavar = 1/ metavar var x end metavar * metavar var x end metavar conclude not0 0 <= 1/ metavar var x end metavar imply not0 not0 0 = 1/ metavar var x end metavar end quote state proof state cache var c end expand end define