Nuprl Lemma : rroot_wf
∀[i:{2...}]. ∀[x:{x:ℝ| (↑isEven(i)) ⇒ (r0 ≤ x)} ]. (rroot(i;x) ∈ {y:ℝ| ((↑isEven(i)) ⇒ (r0 ≤ y)) ∧ (y^i = x)} )
Proof
Definitions occuring in Statement :
rroot: rroot(i;x),
rleq: x ≤ y,
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
real: ℝ,
isEven: isEven(n),
int_upper: {i...},
assert: ↑b,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rroot: rroot(i;x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
assert: ↑b,
bfalse: ff,
subtype_rel: A ⊆r B,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
true: True,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
guard: {T},
int-to-real: r(n),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
le: A ≤ B,
top: Top,
sq_type: SQType(T),
bnot: ¬bb,
bor: p ∨bq,
real: ℝ,
bdd-diff: bdd-diff(f;g),
rroot-abs: rroot-abs(i;x),
rminus: -(x),
rroot-odd: rroot-odd(i;x),
has-value: (a)↓,
absval: |i|,
subtract: n - m,
int_seg: {i..j-},
lelt: i ≤ j < k,
req: x = y,
rless: x < y,
sq_exists: ∃x:A [B[x]],
accelerate: accelerate(k;f),
nequal: a ≠ b ∈ T ,
int_nzero: ℤ-o,
sq_stable: SqStable(P)
Latex:
\mforall{}[i:\{2...\}]. \mforall{}[x:\{x:\mBbbR{}| (\muparrow{}isEven(i)) {}\mRightarrow{} (r0 \mleq{} x)\} ].
(rroot(i;x) \mmember{} \{y:\mBbbR{}| ((\muparrow{}isEven(i)) {}\mRightarrow{} (r0 \mleq{} y)) \mwedge{} (y\^{}i = x)\} )
Date html generated:
2020_05_20-PM-00_31_20
Last ObjectModification:
2020_01_03-PM-06_51_56
Theory : reals
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