### Nuprl Lemma : fps-elim-x-mul

`∀[X:Type]`
`  ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[x:X]. ∀[f,g:PowerSeries(X;r)].  ((f*g)(x:=0) = (f(x:=0)*g(x:=0)) ∈ PowerSeries(X;r)) `
`  supposing valueall-type(X)`

Proof

Definitions occuring in Statement :  fps-elim-x: `f(x:=0)` fps-mul: `(f*g)` power-series: `PowerSeries(X;r)` deq: `EqDecider(T)` valueall-type: `valueall-type(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T` crng: `CRng`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` fun_thru_2op: `FunThru2op(A;B;opa;opb;f)` infix_ap: `x f y` fps-elim-x: `f(x:=0)` and: `P ∧ Q`
Lemmas referenced :  fps-elim-hom crng_wf deq_wf power-series_wf valueall-type_wf
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality introduction independent_isectElimination sqequalRule productElimination isect_memberEquality axiomEquality universeEquality

Latex:
\mforall{}[X:Type]
\mforall{}[eq:EqDecider(X)].  \mforall{}[r:CRng].  \mforall{}[x:X].  \mforall{}[f,g:PowerSeries(X;r)].
((f*g)(x:=0)  =  (f(x:=0)*g(x:=0)))
supposing  valueall-type(X)

Date html generated: 2016_05_15-PM-09_53_20
Last ObjectModification: 2015_12_27-PM-04_37_49

Theory : power!series

Home Index