Nuprl Lemma : interval-totally-bounded
∀a:ℝ. ∀b:{b:ℝ| a ≤ b} . totally-bounded(λx.(x ∈ [a, b]))
Proof
Definitions occuring in Statement :
rccint: [l, u],
i-member: r ∈ I,
totally-bounded: totally-bounded(A),
rleq: x ≤ y,
real: ℝ,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
lambda: λx.A[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
totally-bounded: totally-bounded(A),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
exists: ∃x:A. B[x],
guard: {T},
sq_type: SQType(T),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
rneq: x ≠ y,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
ge: i ≥ j ,
sq_exists: ∃x:A [B[x]],
rless: x < y,
nat_plus: ℕ+,
squash: ↓T,
sq_stable: SqStable(P),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top,
true: True,
less_than': less_than'(a;b),
less_than: a < b,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
rdiv: (x/y),
rset: Set(ℝ),
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
i-member: r ∈ I,
rccint: [l, u],
rset-member: x ∈ A,
real: ℝ,
subtract: n - m,
rge: x ≥ y,
rgt: x > y
Latex:
\mforall{}a:\mBbbR{}. \mforall{}b:\{b:\mBbbR{}| a \mleq{} b\} . totally-bounded(\mlambda{}x.(x \mmember{} [a, b]))
Date html generated:
2020_05_20-AM-11_31_16
Last ObjectModification:
2020_01_06-PM-00_46_40
Theory : reals
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