Nuprl Lemma : infinity-norm-rneq-real-vec-sep
∀n:ℕ+. ∀x,v:ℝ^n. (||v||∞ ≠ ||x||∞ ⇒ x ≠ v)
Proof
Definitions occuring in Statement :
real-vec-infinity-norm: ||v||∞,
real-vec-sep: a ≠ b,
real-vec: ℝ^n,
rneq: x ≠ y,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
int_seg: {i..j-},
lelt: i ≤ j < k,
real-vec: ℝ^n,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtract: n - m,
nequal: a ≠ b ∈ T ,
eq_int: (i =z j),
rless: x < y,
sq_exists: ∃x:A [B[x]]
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}x,v:\mBbbR{}\^{}n. (||v||\minfty{} \mneq{} ||x||\minfty{} {}\mRightarrow{} x \mneq{} v)
Date html generated:
2020_05_20-PM-00_48_08
Last ObjectModification:
2019_11_11-PM-09_16_11
Theory : reals
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