Nuprl Lemma : max-metric-mdist-from-zero-rless
∀c:{c:ℝ| r0 < c} . ∀n:ℕ. ∀x:ℝ^n. ((∀i:ℕn. (|x i| < c)) ⇒ (mdist(max-metric(n);x;λi.r0) < c))
Proof
Definitions occuring in Statement :
max-metric: max-metric(n),
real-vec: ℝ^n,
mdist: mdist(d;x;y),
rless: x < y,
rabs: |x|,
int-to-real: r(n),
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
prop: ℙ,
guard: {T},
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Latex:
\mforall{}c:\{c:\mBbbR{}| r0 < c\} . \mforall{}n:\mBbbN{}. \mforall{}x:\mBbbR{}\^{}n. ((\mforall{}i:\mBbbN{}n. (|x i| < c)) {}\mRightarrow{} (mdist(max-metric(n);x;\mlambda{}i.r0) < c))
Date html generated:
2020_05_20-PM-00_43_13
Last ObjectModification:
2019_11_21-AM-06_13_40
Theory : reals
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