Logiweb aspects of lemma telescopeNumerical base in pyk

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The predefined "pyk" aspect

define pyk of lemma telescopeNumerical base 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 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 capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode space unicode small b unicode small a unicode small s unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma telescopeNumerical base as text unicode start of text 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 capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode left parenthesis unicode capital b unicode small a unicode small s unicode small e 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 telescopeNumerical base as system Q infer all metavar var m end metavar indeed | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | <= UStelescope( metavar var m end metavar , 0 ) end define

The user defined "the proof aspect" aspect

define proof of lemma telescopeNumerical base as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed lemma eqReflexivity conclude 0 = 0 cut 1rule UStelescope zero modus ponens 0 = 0 conclude UStelescope( metavar var m end metavar , 0 ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | cut lemma eqReflexivity conclude metavar var m end metavar = metavar var m end metavar cut lemma plus0Left conclude 0 + 1 = 1 cut lemma eqAdditionLeft modus ponens 0 + 1 = 1 conclude metavar var m end metavar + 0 + 1 = metavar var m end metavar + 1 cut lemma eqSymmetry modus ponens metavar var m end metavar + 0 + 1 = metavar var m end metavar + 1 conclude metavar var m end metavar + 1 = metavar var m end metavar + 0 + 1 cut lemma sameSeries(NumDiff) modus ponens metavar var m end metavar = metavar var m end metavar modus ponens metavar var m end metavar + 1 = metavar var m end metavar + 0 + 1 conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | cut lemma eqTransitivity modus ponens UStelescope( metavar var m end metavar , 0 ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | modus ponens | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | conclude UStelescope( metavar var m end metavar , 0 ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | cut lemma eqSymmetry modus ponens UStelescope( metavar var m end metavar , 0 ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | = UStelescope( metavar var m end metavar , 0 ) cut lemma eqLeq modus ponens | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | = UStelescope( metavar var m end metavar , 0 ) conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 0 + 1 ] | <= UStelescope( metavar var m end metavar , 0 ) end quote state proof state cache var c end expand end define