Logiweb aspects of lemma telescopeNumerical indu in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma telescopeNumerical 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 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 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 telescopeNumerical indu 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 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 telescopeNumerical indu as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar ) imply | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) end define

The user defined "the proof aspect" aspect

define proof of lemma telescopeNumerical 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 n end metavar indeed | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar ) infer lemma +1IsPositive(N) conclude not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 cut 1rule UStelescope positive modus ponens not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 conclude UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) cut lemma x=x+y-y conclude metavar var n end metavar = metavar var n end metavar + 1 + - 1 cut lemma eqSymmetry modus ponens metavar var n end metavar = metavar var n end metavar + 1 + - 1 conclude metavar var n end metavar + 1 + - 1 = metavar var n end metavar cut lemma sameTelescope second modus ponens metavar var n end metavar + 1 + - 1 = metavar var n end metavar conclude UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n end metavar ) cut lemma eqAdditionLeft modus ponens UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = UStelescope( metavar var m end metavar , metavar var n end metavar ) conclude | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) cut lemma eqTransitivity modus ponens UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) modus ponens | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) conclude UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) cut lemma eqSymmetry modus ponens UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) = | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) conclude | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) = UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) cut lemma leqAdditionLeft modus ponens | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar ) conclude | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) cut lemma subLeqRight modus ponens | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) = UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) modus ponens | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar ) conclude | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) cut axiom plusCommutativity conclude | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | cut lemma subLeqLeft modus ponens | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | modus ponens | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | + | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) cut lemma insertMiddleTerm(Numerical) conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | cut lemma leqTransitivity modus ponens | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | modus ponens | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + | [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) cut all metavar var m end metavar indeed all metavar var n end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n end metavar indeed | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar ) infer | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) conclude | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar ) imply | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 + 1 ] | <= UStelescope( metavar var m end metavar , metavar var n end metavar + 1 ) end quote state proof state cache var c end expand end define