Nuprl Lemma : rinv1
rinv(r1) = r1
Proof
Definitions occuring in Statement :
rinv: rinv(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
rnonzero: rnonzero(x),
exists: ∃x:A. B[x],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
absval: |i|,
int-to-real: r(n),
subtype_rel: A ⊆r B,
real: ℝ,
nat: ℕ,
uimplies: b supposing a,
uiff: uiff(P;Q)
Lemmas referenced :
rmul-rinv1,
int-to-real_wf,
less_than_wf,
absval_wf,
real_wf,
nat_wf,
rmul_wf,
rinv_wf,
req_functionality,
rmul-one-both,
req_weakening
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
independent_functionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
productElimination
Latex:
rinv(r1) = r1
Date html generated:
2017_10_02-PM-07_17_28
Last ObjectModification:
2017_04_06-AM-00_28_07
Theory : reals
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