r:Rng, a, b, c:|r|. ((a +r b) = (a +r c)  |r|)  (b = c) 

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Up	rings 1
Definitions of Statement	Rng, r+gp
Definitions	IMonoid, t  T, IGroup, x:A. B(x), t.2, t.1, , P & Q, Mon, Group{i}, r+gp, *, |g|
Lemmas	rng wf, grp wf, grp inv wf, inverse wf, grp id wf, grp op wf, grp car wf, monoid p wf, add grp of rng wf a, grp op cancel l