Nuprl Lemma : int-rdiv-rless-witness2
∀k:ℕ+. (3 * k ∈ (r1)/k < (r(2))/k)
Proof
Definitions occuring in Statement :
rless: x < y,
int-rdiv: (a)/k1,
int-to-real: r(n),
nat_plus: ℕ+,
all: ∀x:A. B[x],
member: t ∈ T,
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
int-to-real: r(n),
int-rdiv: (a)/k1,
rless: x < y,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:A [B[x]],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
has-value: (a)↓
Latex:
\mforall{}k:\mBbbN{}\msupplus{}. (3 * k \mmember{} (r1)/k < (r(2))/k)
Date html generated:
2020_05_20-AM-10_56_41
Last ObjectModification:
2019_12_28-PM-08_05_05
Theory : reals
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