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