Nuprl Lemma : real-vec-infinity-norm-req
∀[n:ℕ+]. ∀[v:ℝ^n]. (||v||∞ = if (n =z 1) then |v 0| else rmax(||v||∞;|v (n - 1)|) fi )
Proof
Definitions occuring in Statement :
real-vec-infinity-norm: ||v||∞,
real-vec: ℝ^n,
rabs: |x|,
rmax: rmax(x;y),
req: x = y,
nat_plus: ℕ+,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
apply: f a,
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
nat: ℕ,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
real-vec-infinity-norm: ||v||∞,
max-metric: max-metric(n),
mdist: mdist(d;x;y),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
le: A ≤ B,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top,
subtract: n - m
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[v:\mBbbR{}\^{}n]. (||v||\minfty{} = if (n =\msubz{} 1) then |v 0| else rmax(||v||\minfty{};|v (n - 1)|) fi )
Date html generated:
2020_05_20-PM-00_47_39
Last ObjectModification:
2020_01_06-PM-00_23_29
Theory : reals
Home
Index