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

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Up	rings 1
Definitions of Statement	Rng, r+gp
Definitions	IMonoid, t  T, IGroup, x f y, P & Q, x:A. B(x), t.2, t.1, , 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 inv assoc