case (calc_dec c c'); [ left | right ].
elim e; auto with arith pts.
red in |- *; intro; apply n.
apply univ_inv with (Sprop c) (Sprop c'); intros; auto with arith pts.
inversion_clear H0; auto with arith pts.
red in |- *; intros.
apply univ_inv with (Sprop c) (Stype c0 n); intros; auto with arith pts.
inversion_clear H0.
red in |- *; intros.
apply univ_inv with (Stype c n) (Sprop c0); intros; auto with arith pts.
inversion_clear H0.
case (calc_dec c c'); intros.
case (le_gt_dec n n'); [ left | right ].
elim e; auto with arith pts.
red in |- *; intros.
apply univ_inv with (Stype c n) (Stype c' n'); intros; auto with arith pts.
inversion_clear H0.
absurd (n <= n'); auto with arith pts.
right; red in |- *; intros; apply n0.
apply univ_inv with (Stype c n) (Stype c' n'); intros; auto with arith pts.
inversion_clear H0; auto with arith pts.
Qed.
(* Inference des axiomes et regles *)

(* Specifications: *)
Lemma ecc_inf_axiom :
forall s : srt_ecc, {sp : srt_ecc | ppal (axiom_ecc s) univ sp}.