Nuprl Lemma : cdrng_is_abdgrp
∀[r:CDRng]. (r↓+gp ∈ AbDGrp)
Proof
Definitions occuring in Statement :
add_grp_of_rng: r↓+gp,
cdrng: CDRng,
abdgrp: AbDGrp,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cdrng: CDRng,
abdgrp: AbDGrp,
crng: CRng,
grp_car: |g|,
pi1: fst(t),
add_grp_of_rng: r↓+gp,
rng_car: |r|,
grp_eq: =b,
pi2: snd(t),
rng_eq: =b,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
prop: ℙ
Lemmas referenced :
cdrng_properties,
cdrng_wf,
add_grp_of_rng_wf_b,
eqfun_p_wf,
grp_car_wf,
grp_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality,
sqequalRule,
because_Cache
Latex:
\mforall{}[r:CDRng]. (r\mdownarrow{}+gp \mmember{} AbDGrp)
Date html generated:
2018_05_21-PM-03_14_38
Last ObjectModification:
2018_05_19-AM-08_07_51
Theory : rings_1
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