Nuprl Lemma : i-member-iff
∀I:Interval. ∀r:ℝ. (r ∈ I ⇐⇒ ∃n:ℕ+. (r ∈ i-approx(I;n)))
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
interval: Interval,
i-approx: i-approx(I;n),
top: Top,
i-member: r ∈ I,
iff: P ⇐⇒ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
prop: ℙ,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
decidable: Dec(P),
true: True,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
le: A ≤ B,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y
Latex:
\mforall{}I:Interval. \mforall{}r:\mBbbR{}. (r \mmember{} I \mLeftarrow{}{}\mRightarrow{} \mexists{}n:\mBbbN{}\msupplus{}. (r \mmember{} i-approx(I;n)))
Date html generated:
2020_05_20-AM-11_32_02
Last ObjectModification:
2019_12_07-PM-04_20_04
Theory : reals
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