Nuprl Lemma : rnexp-mul
∀[n,m:ℕ]. ∀[x:ℝ]. (x^m^n = x^m * n)
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
multiply: n * m
Definitions unfolded in proof :
or: P ∨ Q,
decidable: Dec(P),
less_than': less_than'(a;b),
le: A ≤ B,
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
top: Top,
subtract: n - m,
nequal: a ≠ b ∈ T ,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[x:\mBbbR{}]. (x\^{}m\^{}n = x\^{}m * n)
Date html generated:
2020_05_20-AM-10_59_03
Last ObjectModification:
2019_12_28-AM-11_03_13
Theory : reals
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