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diff --git a/matita/matita/contribs/BTM/character/triple.ma b/matita/matita/contribs/BTM/character/triple.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "character/class_pt.ma".
+
+(* TRIPLES OF CHARACTER CLASSES *********************************************)
+
+lemma not_p_pS: ∀i. P i → P (i + 1) → False.
+#i #Hi #HSi
+elim (p_inv_gen … Hi) -Hi #hi #Hi
+elim (p_inv_gen … HSi) -HSi #hSi #HSi destruct
+lapply (injective_plus_l … HSi) -HSi #H
+elim (not_b_divides_nbr … H) -H //
+qed-.
+
+lemma not_p_pSS: ∀i. P i → P (i + 2) → False.
+#i #Hi #HSi
+elim (p_inv_gen … Hi) -Hi #hi #Hi
+elim (p_inv_gen … HSi) -HSi #hSi #HSi destruct
+>plus_plus_comm_23 in HSi; #H
+lapply (injective_plus_l … H) -H #H
+elim (not_b_divides_nbr … H) -H //
+qed-.
+
+lemma not_p_tS: ∀i. P i → T (i + 1) → False.
+#i #Hp #Ht
+elim (p_inv_gen … Hp) -Hp #hp #Hp
+elim (t_inv_gen … Ht) -Ht #ht #kt #Ht destruct
+>exp_n_m_plus_1 in Ht; <associative_times >associative_plus #H
+elim (not_b_divides_nbr … H) -H //
+qed-.