Logiweb aspects of lemma fromNotSameF(Weak) in pyk

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The predefined "pyk" aspect

define pyk of lemma fromNotSameF(Weak) 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 f unicode small r unicode small o unicode small m unicode capital n unicode small o unicode small t unicode capital s unicode small a unicode small m unicode small e unicode capital f unicode left parenthesis unicode capital w unicode small e unicode small a unicode small k unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromNotSameF(Weak) as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital n unicode small o unicode small t unicode capital s unicode small a unicode small m unicode small e unicode capital f unicode left parenthesis unicode capital w unicode small e unicode small a unicode small k unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromNotSameF(Weak) as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed not0 for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var infer not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromNotSameF(Weak) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed not0 for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var infer 1rule repetition modus ponens not0 for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var conclude not0 for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var cut 1rule deduction modus ponens not0 for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var conclude not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar cut pred lemma AEAnegated modus ponens not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar cut all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar infer prop lemma from negated double imply modus ponens not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar cut prop lemma first conjunct modus ponens not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar cut prop lemma second conjunct modus ponens not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar cut lemma fromNotSameF(Weak)(Helper) modus ponens not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar cut prop lemma join conjuncts modus ponens not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar modus ponens not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar conclude not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar cut 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar infer not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar conclude not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar imply not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar cut pred lemma addEAE modus ponens not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar imply not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar conclude not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar imply not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar cut 1rule mp modus ponens not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar imply not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar modus ponens not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var m end metavar imply not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = metavar var ep end metavar conclude not0 for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var m end metavar indeed not0 not0 not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n end metavar <= metavar var m end metavar imply not0 not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply [ metavar var fy end metavar ; metavar var m end metavar ] <= [ metavar var fx end metavar ; metavar var m end metavar ] + - metavar var ep end metavar end quote state proof state cache var c end expand end define