Nuprl Lemma : rnexp-req-iff-odd
∀n:ℕ+. ∀x,y:ℝ. ((↑isOdd(n)) ⇒ (x = y ⇐⇒ x^n = y^n))
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
real: ℝ,
isOdd: isOdd(n),
nat_plus: ℕ+,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
uimplies: b supposing a,
not: ¬A,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
nat_plus: ℕ+,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_wf,
rleq_antisymmetry,
not-rless,
rnexp-rless-odd,
rless_transitivity1,
rnexp_wf,
rleq_weakening,
rless_irreflexivity,
rless_wf,
req_inversion,
nat_plus_subtype_nat,
assert_wf,
isOdd_wf,
real_wf,
nat_plus_wf,
req_weakening,
req_functionality,
rnexp_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
sqequalRule,
voidElimination,
setElimination,
rename,
productElimination
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}x,y:\mBbbR{}. ((\muparrow{}isOdd(n)) {}\mRightarrow{} (x = y \mLeftarrow{}{}\mRightarrow{} x\^{}n = y\^{}n))
Date html generated:
2016_05_18-AM-07_29_25
Last ObjectModification:
2015_12_28-AM-00_52_30
Theory : reals
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