Nuprl Lemma : assert_of_rng_eq
∀[r:DRng]. ∀[a,b:|r|]. uiff(↑(a =b b);a = b ∈ |r|)
Proof
Definitions occuring in Statement :
drng: DRng,
rng_eq: =b,
rng_car: |r|,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
eqfun_p: IsEqFun(T;eq),
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
infix_ap: x f y,
drng: DRng,
implies: P ⇒ Q
Lemmas referenced :
drng_all_properties,
assert_wf,
rng_eq_wf,
assert_witness,
equal_wf,
rng_car_wf,
drng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
isect_memberEquality,
independent_pairEquality,
axiomEquality,
applyEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[r:DRng]. \mforall{}[a,b:|r|]. uiff(\muparrow{}(a =\msubb{} b);a = b)
Date html generated:
2016_05_15-PM-00_20_38
Last ObjectModification:
2015_12_27-AM-00_02_46
Theory : rings_1
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