Logiweb aspects of lemma fromNotSameF(Strong) helper in pyk

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The predefined "pyk" aspect

define pyk of lemma fromNotSameF(Strong) helper 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 s unicode small t unicode small r unicode small o unicode small n unicode small g unicode right parenthesis unicode space unicode small h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromNotSameF(Strong) helper 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 s unicode small t unicode small r unicode small o unicode small n unicode small g unicode right parenthesis unicode left parenthesis unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r 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(Strong) helper as system Q infer all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar imply for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var v1 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n2 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 ] end define

The user defined "the proof aspect" aspect

define proof of lemma fromNotSameF(Strong) helper as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar infer for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var v1 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar infer metavar var n2 end metavar <= metavar var m 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 n1 end metavar <= metavar var n2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 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 n1 end metavar <= metavar var n2 end metavar cut prop lemma first conjunct modus ponens not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n1 end metavar <= metavar var n2 end metavar conclude not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar cut prop lemma second conjunct modus ponens not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply not0 metavar var n1 end metavar <= metavar var n2 end metavar conclude metavar var n1 end metavar <= metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar conclude not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar cut lemma fromNotLess modus ponens not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar conclude metavar var ep end metavar <= | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | cut lemma a4 at metavar var n2 end metavar modus ponens for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var v1 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar conclude for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var n2 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar cut lemma a4 at metavar var m end metavar modus ponens for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var n2 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar conclude not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var n2 end metavar imply metavar var n1 end metavar <= metavar var m end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar cut lemma positiveHalved modus ponens not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar conclude not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar cut lemma leqTransitivity modus ponens metavar var n1 end metavar <= metavar var n2 end metavar modus ponens metavar var n2 end metavar <= metavar var m end metavar conclude metavar var n1 end metavar <= metavar var m end metavar cut prop lemma mp3 modus ponens not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var n2 end metavar imply metavar var n1 end metavar <= metavar var m end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar modus ponens not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar modus ponens metavar var n1 end metavar <= metavar var n2 end metavar modus ponens metavar var n1 end metavar <= metavar var m end metavar conclude not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar cut prop lemma first conjunct modus ponens not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar conclude not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar cut prop lemma second conjunct modus ponens not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar conclude not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar cut lemma fromNotSameF(Strong) helper2 modus ponens metavar var ep end metavar <= | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | modus ponens not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar modus ponens not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var m end metavar ] | = 1/ 1 + 1 * 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 ] cut all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed 1rule deduction modus ponens all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 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 n1 end metavar <= metavar var n2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar infer for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var v1 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar infer metavar var n2 end metavar <= metavar var m end metavar infer not0 [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] conclude not0 not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n1 end metavar <= metavar var n2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var n2 end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | = metavar var ep end metavar imply for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n1 end metavar <= metavar var v1 end metavar imply metavar var n1 end metavar <= metavar var v2 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | <= 1/ 1 + 1 * metavar var ep end metavar imply not0 not0 | [ metavar var fy end metavar ; metavar var v1 end metavar ] + - [ metavar var fy end metavar ; metavar var v2 end metavar ] | = 1/ 1 + 1 * metavar var ep end metavar imply metavar var n2 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 ] end quote state proof state cache var c end expand end define