Logiweb(TM)

Logiweb aspects of lemma sameFsymmetry in pyk

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The predefined "pyk" aspect

define pyk of lemma sameFsymmetry 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 f unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameFsymmetry as text unicode start of text unicode capital s unicode capital f unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameFsymmetry as system Q infer all metavar var ep end metavar indeed all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar sameF metavar var fy end metavar infer metavar var fy end metavar sameF metavar var fx end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma sameFsymmetry as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var ep end metavar indeed all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar sameF metavar var fy end metavar infer not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar infer existential var var c end var <= metavar var m end metavar infer 1rule fromSameF modus ponens metavar var fx end metavar sameF metavar var fy end metavar modus ponens not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar conclude existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 1rule mp modus ponens existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 modus ponens existential var var c end var <= metavar var m end metavar conclude not0 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 numericalDifference conclude if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] ) = if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] ) cut lemma subLessLeft modus ponens if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] ) = if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] ) modus ponens not0 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 if( 0 <= [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] , - [ 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 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 all metavar var ep end metavar indeed all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed 1rule deduction modus ponens all metavar var ep end metavar indeed all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar sameF metavar var fy end metavar infer not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar infer existential var var c end var <= metavar var m end metavar infer not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 metavar var fx end metavar sameF metavar var fy end metavar imply not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 metavar var fx end metavar sameF metavar var fy end metavar infer 1rule mp modus ponens metavar var fx end metavar sameF metavar var fy end metavar imply not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 metavar var fx end metavar sameF metavar var fy end metavar conclude not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 toSameF modus ponens not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply existential var var c end var <= metavar var m end metavar imply not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 imply not0 not0 if( 0 <= [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , [ metavar var fy end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] , - [ 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 metavar var fy end metavar sameF metavar var fx end metavar end quote state proof state cache var c end expand end define

The pyk compiler, version 0.grue.20060417+ by Klaus Grue,
GRD-2006-09-15.UTC:09:33:20.992497 = MJD-53993.TAI:09:33:53.992497 = LGT-4665029633992497e-6