Nuprl Lemma : rsqrt-is-one
∀[x:ℝ]. uiff((r0 ≤ x) ∧ (rsqrt(x) = r1);x = r1)
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rleq: x ≤ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat: ℕ,
squash: ↓T,
true: True,
guard: {T},
rleq: x ≤ y,
rnonneg: rnonneg(x),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[x:\mBbbR{}]. uiff((r0 \mleq{} x) \mwedge{} (rsqrt(x) = r1);x = r1)
Date html generated:
2020_05_20-PM-00_32_08
Last ObjectModification:
2019_12_14-PM-03_08_05
Theory : reals
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