r:Rng. -r(0) = 0  |r| 

latex

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, e, ~, |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 id