Nuprl Lemma : sq_stable__integ_dom_p
∀[r:CRng]. SqStable(IsIntegDom(r))
Proof
Definitions occuring in Statement :
integ_dom_p: IsIntegDom(r),
crng: CRng,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
integ_dom_p: IsIntegDom(r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
and: P ∧ Q,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
crng: CRng,
rng: Rng,
prop: ℙ,
all: ∀x:A. B[x],
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
rng_car_wf,
rng_zero_wf,
rng_one_wf,
rng_times_wf,
not_wf,
squash_wf,
nequal_wf,
all_wf,
infix_ap_wf,
crng_wf,
sq_stable__and,
sq_stable__not,
sq_stable__all,
sq_stable__equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
voidElimination,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
axiomEquality,
applyEquality,
productEquality,
functionEquality,
isect_memberEquality,
independent_functionElimination,
lambdaFormation,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:CRng]. SqStable(IsIntegDom(r))
Date html generated:
2017_10_01-AM-08_17_35
Last ObjectModification:
2017_02_28-PM-02_02_57
Theory : rings_1
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