Nuprl Lemma : series-diverges-tail
∀x:ℕ ⟶ ℝ. ∀N:ℕ. (Σn.x[N + n]↑ ⇒ Σn.x[n]↑)
Proof
Definitions occuring in Statement :
series-diverges: 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 :
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
so_apply: x[s],
so_lambda: λ2x.t[x],
squash: ↓T,
sq_stable: SqStable(P),
cand: A c∧ B,
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 ,
nat_plus: ℕ+,
sq_exists: ∃x:A [B[x]],
rless: x < y,
uall: ∀[x:A]. B[x],
nat: ℕ,
and: P ∧ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
diverges: n.x[n]↑,
series-diverges: Σn.x[n]↑,
implies: P ⇒ Q,
all: ∀x:A. B[x],
guard: {T},
sq_type: SQType(T),
real: ℝ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
pointwise-req: x[k] = y[k] for k ∈ [n,m]
Latex:
\mforall{}x:\mBbbN{} {}\mrightarrow{} \mBbbR{}. \mforall{}N:\mBbbN{}. (\mSigma{}n.x[N + n]\muparrow{} {}\mRightarrow{} \mSigma{}n.x[n]\muparrow{})
Date html generated:
2020_05_20-AM-11_20_56
Last ObjectModification:
2019_12_28-AM-11_07_14
Theory : reals
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