Nuprl Lemma : int-int-retraction-reals-1
∀k:{2...}. ∃r:(ℤ ⟶ ℤ) ⟶ ℝ. ∀x:ℝ. (accelerate(k;x) = (r (λi.if i <z 1 then x 1 else x i fi )) ∈ ℝ)
Proof
Definitions occuring in Statement :
accelerate: accelerate(k;f),
real: ℝ,
int_upper: {i...},
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[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: ℝ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
int_upper: {i...},
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
regularize: regularize(k;f),
nat: ℕ,
le: A ≤ B,
sq_stable: SqStable(P),
regular-int-seq: k-regular-seq(f),
int_seg: {i..j-},
lelt: i ≤ j < k,
subtract: n - m
Latex:
\mforall{}k:\{2...\}. \mexists{}r:(\mBbbZ{} {}\mrightarrow{} \mBbbZ{}) {}\mrightarrow{} \mBbbR{}. \mforall{}x:\mBbbR{}. (accelerate(k;x) = (r (\mlambda{}i.if i <z 1 then x 1 else x i fi )))
Date html generated:
2020_05_20-PM-00_06_37
Last ObjectModification:
2020_03_14-AM-09_31_25
Theory : reals
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