Nuprl Lemma : real-vec-norm-1-exists
∀[n:ℕ+]. ∃b:ℝ^n. (||b|| = r1)
Proof
Definitions occuring in Statement :
real-vec-norm: ||x||,
real-vec: ℝ^n,
req: x = y,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat_plus: ℕ+,
real-vec-norm: ||x||,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
dot-product: x⋅y,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
less_than: a < b,
squash: ↓T,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mexists{}b:\mBbbR{}\^{}n. (||b|| = r1)
Date html generated:
2020_05_20-PM-00_36_41
Last ObjectModification:
2019_11_10-PM-01_14_44
Theory : reals
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