Nuprl Lemma : cdrng_properties
∀[r:CDRng]. IsEqFun(|r|;=b)
Proof
Definitions occuring in Statement : 
cdrng: CDRng
, 
rng_eq: =b
, 
rng_car: |r|
, 
eqfun_p: IsEqFun(T;eq)
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
eqfun_p: IsEqFun(T;eq)
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
prop: ℙ
, 
infix_ap: x f y
, 
cdrng: CDRng
, 
crng: CRng
, 
rng: Rng
, 
implies: P 
⇒ Q
, 
sq_stable: SqStable(P)
, 
squash: ↓T
Lemmas referenced : 
sq_stable__eqfun_p, 
cdrng_wf, 
rng_car_wf, 
equal_wf, 
assert_witness, 
rng_eq_wf, 
assert_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
thin, 
hypothesisEquality, 
productElimination, 
independent_pairEquality, 
axiomEquality, 
hypothesis, 
lemma_by_obid, 
applyEquality, 
setElimination, 
rename, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
imageMemberEquality, 
baseClosed, 
imageElimination
Latex:
\mforall{}[r:CDRng].  IsEqFun(|r|;=\msubb{})
Date html generated:
2016_05_15-PM-00_20_56
Last ObjectModification:
2016_01_15-AM-08_51_33
Theory : rings_1
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