Nuprl Lemma : rnexp-rmul
∀[n:ℕ]. ∀[x,y:ℝ]. (x * y^n = (x^n * y^n))
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
rmul: a * b,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x]
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,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
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,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}]. (x * y\^{}n = (x\^{}n * y\^{}n))
Date html generated:
2020_05_20-AM-11_00_32
Last ObjectModification:
2020_01_06-PM-00_29_31
Theory : reals
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