Nuprl Lemma : series-converges-tail2
∀N:ℕ. ∀x:ℕ ⟶ ℝ. (Σn.x[n + N]↓ ⇒ Σn.x[n]↓)
Proof
Definitions occuring in Statement :
series-converges: Σn.x[n]↓,
real: ℝ,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
add: n + m
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
rneq: x ≠ y,
nat_plus: ℕ+,
sq_exists: ∃x:A [B[x]],
converges-to: lim n→∞.x[n] = y,
series-sum: Σn.x[n] = a,
prop: ℙ,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
series-converges: Σn.x[n]↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_type: SQType(T),
true: True,
subtract: n - m,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
pointwise-req: x[k] = y[k] for k ∈ [n,m],
subtype_rel: A ⊆r B
Latex:
\mforall{}N:\mBbbN{}. \mforall{}x:\mBbbN{} {}\mrightarrow{} \mBbbR{}. (\mSigma{}n.x[n + N]\mdownarrow{} {}\mRightarrow{} \mSigma{}n.x[n]\mdownarrow{})
Date html generated:
2020_05_20-AM-11_20_00
Last ObjectModification:
2019_12_28-AM-11_06_45
Theory : reals
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