simple induction 1.
simple induction 1; auto with arith pts.
simple destruct x; auto with arith pts.
intros.
apply H4.
apply inv_univ_trans with y.
apply H1; auto with arith pts.
apply H3; auto with arith pts.
Qed.

Lemma ecc_sort_dec : forall s s' : srt_ecc, decide (s = s').
simple destruct s; simple destruct s'; intros; try (right; discriminate).