proposition: Lemma isnonzerorinvel (X : ring) (is : isnonzerorig X) (x : X) (x' : multrinvpair X x) : ((pr1 x') != 0).
proof: Proof. intros. apply (negf (maponpaths (λ a : X, x * a))). assert (e := pr2 x'). change (paths (x * pr1 x') 1) in e. change (neg (paths (x * pr1 x') (x * 0))). rewrite e. rewrite (ringmultx0 X _). apply is. Defined.
imports: UniMath.Algebra.Groups UniMath.Algebra.RigsAndRings