Nuprl Lemma : rinv-of-rinv
∀[x:ℝ]. rinv(rinv(x)) = x supposing x ≠ r0
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rinv: rinv(x),
req: x = y,
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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
rinv-neq-zero,
rmul-inverse-is-rinv,
rinv_wf2,
rmul-rinv2,
req_inversion,
req_witness,
rneq_wf,
int-to-real_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
independent_functionElimination,
hypothesis,
isectElimination,
hypothesisEquality,
independent_isectElimination,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbR{}]. rinv(rinv(x)) = x supposing x \mneq{} r0
Date html generated:
2016_05_18-AM-07_12_17
Last ObjectModification:
2015_12_28-AM-00_40_19
Theory : reals
Home
Index