Nuprl Lemma : rabs-rnexp
∀[n:ℕ]. ∀[x:ℝ]. (|x^n| = |x|^n)
Proof
Definitions occuring in Statement :
rabs: |x|,
rnexp: x^k1,
req: x = y,
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,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
nequal: a ≠ b ∈ T ,
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
top: Top,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbR{}]. (|x\^{}n| = |x|\^{}n)
Date html generated:
2020_05_20-AM-10_59_24
Last ObjectModification:
2020_01_02-PM-02_13_16
Theory : reals
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