Nuprl Lemma : rroot-odd-2-regular
∀i:{2...}. ∀x:ℝ. 2-regular-seq(rroot-odd(i;x))
Proof
Definitions occuring in Statement :
rroot-odd: rroot-odd(i;x),
real: ℝ,
regular-int-seq: k-regular-seq(f),
int_upper: {i...},
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
has-value: (a)↓,
sq_type: SQType(T),
so_apply: x[s],
so_lambda: λ2x.t[x],
less_than': less_than'(a;b),
le: A ≤ B,
nat: ℕ,
rroot-odd: rroot-odd(i;x),
rroot-abs: rroot-abs(i;x),
regular-int-seq: k-regular-seq(f),
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
sq_stable: SqStable(P),
false: False,
prop: ℙ,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
int_upper: {i...},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
real: ℝ,
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x],
ge: i ≥ j ,
assert: ↑b,
bnot: ¬bb,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
less_than: a < b,
subtract: n - m,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}i:\{2...\}. \mforall{}x:\mBbbR{}. 2-regular-seq(rroot-odd(i;x))
Date html generated:
2020_05_20-PM-00_30_38
Last ObjectModification:
2020_03_20-AM-11_01_25
Theory : reals
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