Logiweb aspects of lemma sameTelescope second indu in pyk

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The predefined "pyk" aspect

define pyk of lemma sameTelescope second indu 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 t unicode small e unicode small l unicode small e unicode small s unicode small c unicode small o unicode small p unicode small e unicode space unicode small s unicode small e unicode small c unicode small o unicode small n unicode small d unicode space unicode small i unicode small n unicode small d unicode small u unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameTelescope second indu as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital t unicode small e unicode small l unicode small e unicode small s unicode small c unicode small o unicode small p unicode small e unicode left parenthesis unicode two unicode right parenthesis unicode left parenthesis unicode capital i unicode small n unicode small d unicode small u 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 sameTelescope second indu as system Q infer all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) imply for all objects metavar var n2 end metavar indeed metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma sameTelescope second indu 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 n1 end metavar indeed all metavar var n2 end metavar indeed all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) infer metavar var n1 end metavar + 1 = metavar var n2 end metavar infer lemma +1IsPositive(N) conclude not0 0 <= metavar var n1 end metavar + 1 imply not0 not0 0 = metavar var n1 end metavar + 1 cut 1rule UStelescope positive modus ponens not0 0 <= metavar var n1 end metavar + 1 imply not0 not0 0 = metavar var n1 end metavar + 1 conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) cut lemma x=x+y-y conclude metavar var n1 end metavar = metavar var n1 end metavar + 1 + - 1 cut lemma a4 at metavar var n1 end metavar + 1 + - 1 modus ponens for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude metavar var n1 end metavar = metavar var n1 end metavar + 1 + - 1 imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) cut 1rule mp modus ponens metavar var n1 end metavar = metavar var n1 end metavar + 1 + - 1 imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) modus ponens metavar var n1 end metavar = metavar var n1 end metavar + 1 + - 1 conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) cut lemma eqSymmetry modus ponens UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar ) cut lemma positiveToRight(Eq) modus ponens metavar var n1 end metavar + 1 = metavar var n2 end metavar conclude metavar var n1 end metavar = metavar var n2 end metavar + - 1 cut lemma a4 at metavar var n2 end metavar + - 1 modus ponens for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude metavar var n1 end metavar = metavar var n2 end metavar + - 1 imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) cut 1rule mp modus ponens metavar var n1 end metavar = metavar var n2 end metavar + - 1 imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) modus ponens metavar var n1 end metavar = metavar var n2 end metavar + - 1 conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) cut lemma eqTransitivity modus ponens UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n1 end metavar ) modus ponens UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) cut lemma eqAdditionLeft modus ponens metavar var n1 end metavar + 1 = metavar var n2 end metavar conclude metavar var m end metavar + metavar var n1 end metavar + 1 = metavar var m end metavar + metavar var n2 end metavar cut lemma eqAddition modus ponens metavar var n1 end metavar + 1 = metavar var n2 end metavar conclude metavar var n1 end metavar + 1 + 1 = metavar var n2 end metavar + 1 cut lemma eqAdditionLeft modus ponens metavar var n1 end metavar + 1 + 1 = metavar var n2 end metavar + 1 conclude metavar var m end metavar + metavar var n1 end metavar + 1 + 1 = metavar var m end metavar + metavar var n2 end metavar + 1 cut lemma sameSeries(NumDiff) modus ponens metavar var m end metavar + metavar var n1 end metavar + 1 = metavar var m end metavar + metavar var n2 end metavar modus ponens metavar var m end metavar + metavar var n1 end metavar + 1 + 1 = metavar var m end metavar + metavar var n2 end metavar + 1 conclude | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | cut lemma addEquations modus ponens | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | modus ponens UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) conclude | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) cut lemma subLessRight modus ponens metavar var n1 end metavar + 1 = metavar var n2 end metavar modus ponens not0 0 <= metavar var n1 end metavar + 1 imply not0 not0 0 = metavar var n1 end metavar + 1 conclude not0 0 <= metavar var n2 end metavar imply not0 not0 0 = metavar var n2 end metavar cut 1rule UStelescope positive modus ponens not0 0 <= metavar var n2 end metavar imply not0 not0 0 = metavar var n2 end metavar conclude UStelescope( metavar var m end metavar , metavar var n2 end metavar ) = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) cut lemma eqSymmetry modus ponens UStelescope( metavar var m end metavar , metavar var n2 end metavar ) = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) conclude | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut lemma eqTransitivity4 modus ponens UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) modus ponens | [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n1 end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 + - 1 ) = | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) modus ponens | [ us ; metavar var m end metavar + metavar var n2 end metavar ] + - [ us ; metavar var m end metavar + metavar var n2 end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n2 end metavar + - 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) infer metavar var n1 end metavar + 1 = metavar var n2 end metavar infer UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) imply metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) infer 1rule mp modus ponens for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) imply metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) modus ponens for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut 1rule gen modus ponens metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude for all objects metavar var n2 end metavar indeed metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) infer for all objects metavar var n2 end metavar indeed metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude for all objects metavar var n2 end metavar indeed metavar var n1 end metavar = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) imply for all objects metavar var n2 end metavar indeed metavar var n1 end metavar + 1 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , metavar var n1 end metavar + 1 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) end quote state proof state cache var c end expand end define