Nuprl Lemma : rmul-rinv3
∀[x,a:ℝ]. (x * rinv(x) * a) = a supposing x ≠ r0
Proof
Definitions occuring in Statement :
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rmul_wf,
rinv_wf2,
rneq_wf,
int-to-real_wf,
real_wf,
rmul-identity1,
req_functionality,
req_transitivity,
req_inversion,
rmul_assoc,
rmul_functionality,
rmul-rinv,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,a:\mBbbR{}]. (x * rinv(x) * a) = a supposing x \mneq{} r0
Date html generated:
2017_10_03-AM-08_27_16
Last ObjectModification:
2017_04_04-PM-08_49_38
Theory : reals
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