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Require Import Setoid.
Inductive mynat := z : mynat | s : mynat -> mynat.
Parameter E : mynat -> mynat -> Prop.
Axiom E_equiv : equiv mynat E.
Add Relation mynat E
reflexivity proved by (proj1 E_equiv)
symmetry proved by (proj2 (proj2 E_equiv))
transitivity proved by (proj1 (proj2 E_equiv))
as E_rel.
Notation "x == y" := (E x y) (at level 70).
Goal z == s z -> s z == z. intros H. setoid_rewrite H at 2. reflexivity. Qed.
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