Nuprl Lemma : rmul-inverse-is-rinv
∀[x:ℝ]. ∀[t:ℝ]. t = rinv(x) supposing (x * t) = r1 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
Lemmas referenced :
rmul-one,
rinv_wf2,
req_witness,
req_wf,
rmul_wf,
int-to-real_wf,
real_wf,
rneq_wf,
req_functionality,
rmul_functionality,
req_weakening,
req_inversion,
req_transitivity,
rmul-assoc,
rmul-rinv2,
rmul-one-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[t:\mBbbR{}]. t = rinv(x) supposing (x * t) = r1 supposing x \mneq{} r0
Date html generated:
2016_05_18-AM-07_11_42
Last ObjectModification:
2015_12_28-AM-00_40_35
Theory : reals
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