Nuprl Lemma : accelerate_wf
∀[k:ℕ+]. ∀[f:{f:ℕ+ ⟶ ℤ| k-regular-seq(f)} ]. (accelerate(k;f) ∈ ℝ)
Proof
Definitions occuring in Statement :
accelerate: accelerate(k;f),
real: ℝ,
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
real: ℝ,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
nequal: a ≠ b ∈ T ,
nat_plus: ℕ+,
uimplies: b supposing a,
has-value: (a)↓,
accelerate: accelerate(k;f),
member: t ∈ T,
uall: ∀[x:A]. B[x],
regular-int-seq: k-regular-seq(f),
nat: ℕ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int_nzero: ℤ-o,
sq_type: SQType(T),
decidable: Dec(P),
or: P ∨ Q,
sq_stable: SqStable(P),
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
subtract: n - m,
less_than: a < b,
le: A ≤ B,
less_than': less_than'(a;b)
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[f:\{f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| k-regular-seq(f)\} ]. (accelerate(k;f) \mmember{} \mBbbR{})
Date html generated:
2020_05_20-AM-10_52_55
Last ObjectModification:
2020_03_19-PM-06_34_05
Theory : reals
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