Nuprl Lemma : mul-rinv-as-rdiv
∀[y,a:ℝ]. (a * rinv(y)) = (a/y) supposing y ≠ r0
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rneq: x ≠ y,
rinv: rinv(x),
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
rdiv: (x/y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
req_weakening,
rmul_wf,
rinv_wf2,
req_witness,
rneq_wf,
int-to-real_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
because_Cache,
independent_isectElimination,
natural_numberEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[y,a:\mBbbR{}]. (a * rinv(y)) = (a/y) supposing y \mneq{} r0
Date html generated:
2017_10_03-AM-08_34_20
Last ObjectModification:
2017_04_05-AM-09_48_05
Theory : reals
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