Nuprl Lemma : regularize-regular
∀k:ℕ+. ∀x:{f:ℕ+ ⟶ ℤ| k-regular-seq(f)} . (regularize(k;x) = x ∈ (ℕ+ ⟶ ℤ))
Proof
Definitions occuring in Statement :
regularize: regularize(k;f),
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
regular-int-seq: k-regular-seq(f),
uall: ∀[x:A]. B[x],
nat: ℕ,
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],
false: False,
and: P ∧ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
subtract: n - m
Latex:
\mforall{}k:\mBbbN{}\msupplus{}. \mforall{}x:\{f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| k-regular-seq(f)\} . (regularize(k;x) = x)
Date html generated:
2020_05_20-AM-11_17_44
Last ObjectModification:
2020_03_14-AM-09_31_36
Theory : reals
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