Nuprl Lemma : decidable__rng_eq
∀r:DRng. ∀u,v:|r|. Dec(u = v ∈ |r|)
Proof
Definitions occuring in Statement :
drng: DRng,
rng_car: |r|,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
drng: DRng,
and: P ∧ Q,
eqfun_p: IsEqFun(T;eq),
infix_ap: x f y,
implies: P ⇒ Q,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rng_car_wf,
drng_wf,
drng_properties,
decidable_functionality,
equal_wf,
assert_wf,
rng_eq_wf,
iff_weakening_uiff,
decidable__assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
applyEquality,
independent_functionElimination,
because_Cache,
independent_pairFormation,
dependent_functionElimination
Latex:
\mforall{}r:DRng. \mforall{}u,v:|r|. Dec(u = v)
Date html generated:
2016_05_15-PM-00_20_40
Last ObjectModification:
2015_12_27-AM-00_02_48
Theory : rings_1
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