Nuprl Lemma : exp-series-converges
∀x:ℝ. Σn.(x^n)/(n)!↓
Proof
Definitions occuring in Statement :
series-converges: Σn.x[n]↓,
rnexp: x^k1,
int-rdiv: (a)/k1,
real: ℝ,
fact: (n)!,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
int_upper: {i...},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
squash: ↓T,
rneq: x ≠ y,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
rge: x ≥ y,
nequal: a ≠ b ∈ T ,
subtract: n - m,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
le: A ≤ B
Latex:
\mforall{}x:\mBbbR{}. \mSigma{}n.(x\^{}n)/(n)!\mdownarrow{}
Date html generated:
2020_05_20-AM-11_26_54
Last ObjectModification:
2020_01_06-PM-00_34_55
Theory : reals
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