Nuprl Lemma : prime_ideal_p_wf
∀[r:RngSig]. ∀[P:|r| ⟶ ℙ]. (IsPrimeIdeal(r;P) ∈ ℙ)
Proof
Definitions occuring in Statement :
prime_ideal_p: IsPrimeIdeal(R;P),
rng_car: |r|,
rng_sig: RngSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
prime_ideal_p: IsPrimeIdeal(R;P),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
and_wf,
not_wf,
rng_one_wf,
all_wf,
rng_car_wf,
rng_times_wf,
or_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r:RngSig]. \mforall{}[P:|r| {}\mrightarrow{} \mBbbP{}]. (IsPrimeIdeal(r;P) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_24_43
Last ObjectModification:
2015_12_27-AM-00_00_10
Theory : rings_1
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