### 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

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