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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