Nuprl Lemma : rnexp-req-iff
∀n:ℕ+. ∀x,y:ℝ. ((r0 ≤ x) ⇒ (r0 ≤ y) ⇒ (x = y ⇐⇒ x^n = y^n))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
natural_number: $n
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,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
guard: {T}
Lemmas referenced :
req_wf,
rnexp_wf,
nat_plus_subtype_nat,
rleq_wf,
int-to-real_wf,
real_wf,
nat_plus_wf,
req_weakening,
req_functionality,
rnexp_functionality,
rleq_antisymmetry,
rnexp-rleq-iff,
rleq_weakening,
req_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
because_Cache,
natural_numberEquality,
independent_isectElimination,
productElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}x,y:\mBbbR{}. ((r0 \mleq{} x) {}\mRightarrow{} (r0 \mleq{} y) {}\mRightarrow{} (x = y \mLeftarrow{}{}\mRightarrow{} x\^{}n = y\^{}n))
Date html generated:
2016_05_18-AM-07_19_42
Last ObjectModification:
2015_12_28-AM-00_46_32
Theory : reals
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