Local Ltac t_eqb :=
  repeat first [ congruence
               | progress subst
               | apply conj
               | match goal with
                 | [ |- context[eqb ?x ?y] ] => destruct (eqb_spec x y)
                 end
               | intro ].

Lemma eqb_compat: Morphisms.Proper (Morphisms.respectful eq (Morphisms.respectful eq eq)) eqb.