Nuprl Lemma : cdrng_is_abdmonoid
∀[r:CDRng]. ((r↓+gp ∈ AbDMon) ∧ (r↓xmn ∈ AbDMon))
Proof
Definitions occuring in Statement :
add_grp_of_rng: r↓+gp,
mul_mon_of_rng: r↓xmn,
cdrng: CDRng,
abdmonoid: AbDMon,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
cdrng: CDRng,
crng: CRng,
comm: Comm(T;op),
abdmonoid: AbDMon,
dmon: DMon,
subtype_rel: A ⊆r B,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
grp_eq: =b,
pi2: snd(t),
mon: Mon,
prop: ℙ,
grp_op: *,
mul_mon_of_rng: r↓xmn
Lemmas referenced :
cdrng_properties,
rng_plus_comm,
add_grp_of_rng_wf_a,
grp_subtype_mon,
eqfun_p_wf,
grp_car_wf,
grp_eq_wf,
comm_wf,
grp_op_wf,
mul_mon_of_rng_wf_a,
crng_properties,
cdrng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
applyEquality,
sqequalRule
Latex:
\mforall{}[r:CDRng]. ((r\mdownarrow{}+gp \mmember{} AbDMon) \mwedge{} (r\mdownarrow{}xmn \mmember{} AbDMon))
Date html generated:
2018_05_21-PM-03_14_36
Last ObjectModification:
2018_05_19-AM-08_07_55
Theory : rings_1
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