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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq_fleq.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq_fleq.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 "basic_2A/multiple/lleq_lleq.ma".
+include "basic_2A/multiple/fleq.ma".
+
+(* LAZY EQUIVALENCE FOR CLOSURES  *******************************************)
+
+(* Main properties **********************************************************)
+
+theorem fleq_trans: ∀l. tri_transitive … (fleq l).
+#l #G1 #G #L1 #L #T1 #T * -G -L -T
+#L #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
+/3 width=3 by lleq_trans, fleq_intro/
+qed-.
+
+theorem fleq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2,l.
+                      ⦃G, L, T⦄ ≡[l] ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≡[l] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
+/3 width=5 by fleq_trans, fleq_sym/ qed-.
+
+theorem fleq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T,l.
+                      ⦃G1, L1, T1⦄ ≡[l] ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≡[l] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
+/3 width=5 by fleq_trans, fleq_sym/ qed-.