Lemma intdomax2r (X : intdom) (x y : X) (is : x * y = 0) (ne : y != 0) : x = 0. Proof. intros. set (int := intdomax X _ _ is). generalize ne. assert (int' : isaprop (y != 0 → x = 0)). { apply impred. intro. apply (setproperty X _ _). } generalize int. simpl. apply (@hinhuniv _ (make_hProp _ int')). intro ene. induction ene as [ e'' | ne' ]. - intro. apply e''. - induction (ne ne'). Defined.
Require Import UniMath.Algebra.Groups.