Nuprl Lemma : rnexp-int
∀[k:ℕ]. ∀[z:ℤ]. (r(z)^k = r(z^k))
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
exp: i^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtract: n - m,
nequal: a ≠ b ∈ T ,
nat_plus: ℕ+,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[z:\mBbbZ{}]. (r(z)\^{}k = r(z\^{}k))
Date html generated:
2020_05_20-AM-10_55_45
Last ObjectModification:
2019_12_14-PM-00_53_47
Theory : reals
Home
Index