Nuprl Lemma : add_grp_of_rng_wf_b
∀[r:Rng]. (r↓+gp ∈ AbGrp)
Proof
Definitions occuring in Statement :
add_grp_of_rng: r↓+gp,
rng: Rng,
abgrp: AbGrp,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
prop: ℙ,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
comm: Comm(T;op),
rng: Rng
Lemmas referenced :
rng_wf,
comm_wf,
grp_car_wf,
grp_op_wf,
add_grp_of_rng_wf_a,
rng_plus_comm,
rng_car_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
dependent_set_memberEquality,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r:Rng]. (r\mdownarrow{}+gp \mmember{} AbGrp)
Date html generated:
2016_05_15-PM-00_21_53
Last ObjectModification:
2015_12_27-AM-00_01_48
Theory : rings_1
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