Nuprl Lemma : ideal_wf
∀[r:CRng]. (Ideal(r){i} ∈ 𝕌')
Proof
Definitions occuring in Statement :
ideal: Ideal(r){i},
crng: CRng,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ideal: Ideal(r){i},
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng,
rng: Rng,
prop: ℙ
Lemmas referenced :
rng_car_wf,
ideal_p_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setEquality,
functionEquality,
cumulativity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:CRng]. (Ideal(r)\{i\} \mmember{} \mBbbU{}')
Date html generated:
2016_05_15-PM-00_22_55
Last ObjectModification:
2015_12_27-AM-00_00_58
Theory : rings_1
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