Nuprl Lemma : rdiv-factorial-lemma1
∀n:ℕ. ((r((2 * (n + 1))!)/r((2 * n)!)) = r(((n * 2) + 2) * ((n * 2) + 1)))
Proof
Definitions occuring in Statement :
rdiv: (x/y),
req: x = y,
int-to-real: r(n),
fact: (n)!,
nat: ℕ,
all: ∀x:A. B[x],
multiply: n * m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
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,
nat_plus: ℕ+,
uiff: uiff(P;Q),
subtract: n - m
Latex:
\mforall{}n:\mBbbN{}. ((r((2 * (n + 1))!)/r((2 * n)!)) = r(((n * 2) + 2) * ((n * 2) + 1)))
Date html generated:
2020_05_20-AM-11_23_44
Last ObjectModification:
2020_01_02-PM-02_10_16
Theory : reals
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