Nuprl Lemma : fun-series-converges_wf
∀[I:Interval]. ∀[f:ℕ ⟶ I ⟶ℝ]. (Σn.f[n;x]↓ for x ∈ I ∈ ℙ)
Proof
Definitions occuring in Statement :
fun-series-converges: Σn.f[n; x]↓ for x ∈ I,
rfun: I ⟶ℝ,
interval: Interval,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fun-series-converges: Σn.f[n; x]↓ for x ∈ I,
so_lambda: λ2x y.t[x; y],
label: ...$L... t,
rfun: I ⟶ℝ,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
fun-converges_wf,
rsum_wf,
int_seg_subtype_nat,
false_wf,
rfun_wf,
int_seg_wf,
real_wf,
i-member_wf,
nat_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
applyEquality,
addEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
hypothesis,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I:Interval]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} I {}\mrightarrow{}\mBbbR{}]. (\mSigma{}n.f[n;x]\mdownarrow{} for x \mmember{} I \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-09_55_04
Last ObjectModification:
2015_12_27-PM-11_08_16
Theory : reals
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