Nuprl Lemma : integ_dom_p_wf
∀[r:CRng]. (IsIntegDom(r) ∈ ℙ)
Proof
Definitions occuring in Statement :
integ_dom_p: IsIntegDom(r),
crng: CRng,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
integ_dom_p: IsIntegDom(r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
crng: CRng,
rng: Rng,
nequal: a ≠ b ∈ T ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
nequal_wf,
rng_car_wf,
rng_zero_wf,
rng_one_wf,
all_wf,
not_wf,
equal_wf,
infix_ap_wf,
rng_times_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:CRng]. (IsIntegDom(r) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_17_33
Last ObjectModification:
2017_02_28-PM-02_02_40
Theory : rings_1
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