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
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