Lemma isnonzerolinvel (X : ring) (is : isnonzerorig X) (x : X) (x' : multlinvpair X x) : ((pr1 x') != 0). Proof. intros. apply (negf (maponpaths (λ a : X, a * x))). assert (e := pr2 x'). change (pr1 x' * x = 1) in e. change (pr1 x' * x != 0 * x). rewrite e. rewrite (ringmult0x X _). apply is. Defined.
Require Import UniMath.Algebra.Groups.