proposition: Lemma isnonzerofromrinvel (X : ring) (is : isnonzerorig X) (x : X) (x' : multrinvpair X x) : x != 0.
proof: Proof. intros. apply (negf (maponpaths (λ a : X, a * (pr1 x')))). assert (e := pr2 x'). change (paths (x * pr1 x') 1) in e. change (neg (paths (x * pr1 x') (0 * (pr1 x')))). rewrite e. rewrite (ringmult0x X _). apply is. Defined.
imports: UniMath.Algebra.Groups UniMath.Algebra.RigsAndRings