Nuprl Lemma : real-vec-sep-0-iff
∀n:ℕ. ∀x:ℝ^n. (x ≠ λi.r0 ⇐⇒ r0 < x⋅x)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
dot-product: x⋅y,
real-vec: ℝ^n,
rless: x < y,
int-to-real: r(n),
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
lambda: λx.A[x],
natural_number: $n
Definitions unfolded in proof :
real-vec-sep: a ≠ b,
real-vec-dist: d(x;y),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
req-vec: req-vec(n;x;y),
real-vec-sub: X - Y,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
real-vec: ℝ^n,
prop: ℙ,
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
uiff: uiff(P;Q),
uimplies: b supposing a,
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
real-vec-norm: ||x||
Latex:
\mforall{}n:\mBbbN{}. \mforall{}x:\mBbbR{}\^{}n. (x \mneq{} \mlambda{}i.r0 \mLeftarrow{}{}\mRightarrow{} r0 < x\mcdot{}x)
Date html generated:
2020_05_20-PM-00_45_54
Last ObjectModification:
2019_12_14-PM-03_03_07
Theory : reals
Home
Index