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