Nuprl Lemma : fps-sub-slice
∀[X:Type]. ∀[r:CRng]. ∀[n:ℤ]. ∀[f,g:PowerSeries(X;r)]. ([(f-g)]_n = ([f]_n-[g]_n) ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-slice: [f]_n,
fps-sub: (f-g),
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-sub: (f-g),
true: True,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
power-series_wf,
crng_wf,
fps-neg_wf,
fps-slice_wf,
fps-add_wf,
equal_wf,
squash_wf,
true_wf,
fps-add-slice,
fps-neg-slice,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
intEquality,
universeEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[n:\mBbbZ{}]. \mforall{}[f,g:PowerSeries(X;r)]. ([(f-g)]\_n = ([f]\_n-[g]\_n))
Date html generated:
2018_05_21-PM-09_56_10
Last ObjectModification:
2017_07_26-PM-06_32_55
Theory : power!series
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