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 calc_dec : forall c c' : calc, decide (c = c').
simple destruct c; simple destruct c';
(right; discriminate) || auto with arith pts.