Logiweb aspects of lemma sameTelescope second in pyk

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The predefined "pyk" aspect

define pyk of lemma sameTelescope second 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameTelescope second 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameTelescope second 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 metavar var n1 end metavar = metavar var n2 end metavar infer UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = 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 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 metavar var n1 end metavar = metavar var n2 end metavar infer lemma sameTelescope second base 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 ) cut lemma sameTelescope second indu 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 ) cut lemma induction modus ponens 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 ) 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 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 ) cut lemma a4 at 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 = 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 ) cut 1rule mp modus ponens 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 ) modus ponens metavar var n1 end metavar = metavar var n2 end metavar conclude UStelescope( metavar var m end metavar , metavar var n1 end metavar ) = UStelescope( metavar var m end metavar , metavar var n2 end metavar ) end quote state proof state cache var c end expand end define