Nuprl Lemma : epsilon/2-lemma
∀[k:ℕ+]. (((r1/r(2 * k)) + (r1/r(2 * k))) ≤ (r1/r(k)))
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rleq: x ≤ y,
radd: a + b,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat_plus: ℕ+,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
top: Top
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. (((r1/r(2 * k)) + (r1/r(2 * k))) \mleq{} (r1/r(k)))
Date html generated:
2020_05_20-AM-11_06_25
Last ObjectModification:
2019_12_12-AM-10_03_48
Theory : reals
Home
Index