Logiweb aspects of lemma sameTelescope second base in pyk

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The predefined "pyk" aspect

define pyk of lemma sameTelescope second 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 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 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 sameTelescope second base 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 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 sameTelescope second base as system Q infer all metavar var m end metavar indeed all metavar var n2 end metavar indeed for all objects metavar var n2 end metavar indeed 0 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , 0 ) = 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 base 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 n2 end metavar indeed 0 = metavar var n2 end metavar infer lemma eqSymmetry modus ponens 0 = metavar var n2 end metavar conclude metavar var n2 end metavar = 0 cut 1rule UStelescope zero modus ponens metavar var n2 end metavar = 0 conclude UStelescope( metavar var m end metavar , metavar var n2 end metavar ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m 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 ] + - [ us ; metavar var m end metavar + 1 ] | conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut lemma UStelescope zero exact conclude UStelescope( metavar var m end metavar , 0 ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 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 ] | = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude UStelescope( metavar var m end metavar , 0 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut all metavar var m end metavar indeed all metavar var n2 end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n2 end metavar indeed 0 = metavar var n2 end metavar infer UStelescope( metavar var m end metavar , 0 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude 0 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , 0 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) cut 1rule gen modus ponens 0 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , 0 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) conclude for all objects metavar var n2 end metavar indeed 0 = metavar var n2 end metavar imply UStelescope( metavar var m end metavar , 0 ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) end quote state proof state cache var c end expand end define