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