Nuprl Lemma : rnexp-rdiv
∀[y,x:ℝ]. ∀[n:ℕ]. ((y^n/x^n) = (y/x)^n) supposing x ≠ r0
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rneq: x ≠ y,
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rdiv: (x/y),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rdiv_wf,
rpower-nonzero,
rnexp_wf,
nat_wf,
rneq_wf,
int-to-real_wf,
real_wf,
inverse-rpower,
rinv_wf2,
req_functionality,
req_inversion,
rinv-as-rdiv,
rnexp_functionality,
rmul_wf,
rmul_functionality,
req_weakening,
rnexp-rmul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
sqequalRule,
isect_memberEquality,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination
Latex:
\mforall{}[y,x:\mBbbR{}]. \mforall{}[n:\mBbbN{}]. ((y\^{}n/x\^{}n) = (y/x)\^{}n) supposing x \mneq{} r0
Date html generated:
2017_10_03-AM-08_37_19
Last ObjectModification:
2017_07_28-AM-07_30_02
Theory : reals
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