Nuprl Lemma : real-approx
∀[x:ℝ]. ∀[n:ℕ+]. (|(r(2 * n) * x) - r(x n)| ≤ r(2))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rabs: |x|,
rsub: x - y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
apply: f a,
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
nat_plus: ℕ+,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
real: ℝ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
rsub: x - y,
subtype_rel: A ⊆r B,
reg-seq-add: reg-seq-add(x;y),
rminus: -(x),
rabs: |x|,
nat: ℕ,
int-to-real: r(n),
reg-seq-mul: reg-seq-mul(x;y),
rnonneg2: rnonneg2(x),
int_upper: {i...},
guard: {T},
subtract: n - m,
sq_stable: SqStable(P),
squash: ↓T,
regular-int-seq: k-regular-seq(f),
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than': less_than'(a;b),
absval: |i|,
sq_type: SQType(T),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
true: True
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. (|(r(2 * n) * x) - r(x n)| \mleq{} r(2))
Date html generated:
2020_05_20-AM-11_03_29
Last ObjectModification:
2019_11_25-PM-00_25_12
Theory : reals
Home
Index