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diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma
deleted file mode 100644
index fda5cbabd..000000000
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma
+++ /dev/null
@@ -1,132 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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-2/substitution/tps_lift.ma".
-
-(* PARALLEL SUBSTITUTION ON TERMS *******************************************)
-
-(* Main properties **********************************************************)
-
-(* Basic-1: was: subst1_confluence_eq *)
-theorem tps_conf_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ≫ T1 →
-                     ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫ T2 →
-                     ∃∃T. L ⊢ T1 [d2, e2] ≫ T & L ⊢ T2 [d1, e1] ≫ T.
-#L #T0 #T1 #d1 #e1 #H elim H -H L T0 T1 d1 e1
-[ /2/
-| #L #K1 #V1 #T1 #i0 #d1 #e1 #Hd1 #Hde1 #HLK1 #HVT1 #T2 #d2 #e2 #H
-  elim (tps_inv_lref1 … H) -H
-  [ #HX destruct -T2 /4/
-  | -Hd1 Hde1 * #K2 #V2 #_ #_ #HLK2 #HVT2
-    lapply (drop_mono … HLK1 … HLK2) -HLK1 HLK2 #H destruct -V1 K1
-    >(lift_mono … HVT1 … HVT2) -HVT1 HVT2 /2/
-  ]
-| #L #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #X #d2 #e2 #HX
-  elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  lapply (tps_leq_repl_dx … HT02 (L. 𝕓{I} V1) ?) -HT02 /2/ #HT02  
-  elim (IHV01 … HV02) -IHV01 HV02 #V #HV1 #HV2
-  elim (IHT01 … HT02) -IHT01 HT02 #T #HT1 #HT2
-  lapply (tps_leq_repl_dx … HT1 (L. 𝕓{I} V) ?) -HT1 /2/
-  lapply (tps_leq_repl_dx … HT2 (L. 𝕓{I} V) ?) -HT2 /3 width=5/
-| #L #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #X #d2 #e2 #HX
-  elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  elim (IHV01 … HV02) -IHV01 HV02;
-  elim (IHT01 … HT02) -IHT01 HT02 /3 width=5/
-]
-qed.
-
-(* Basic-1: was: subst1_confluence_neq *)
-theorem tps_conf_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ≫ T1 →
-                      ∀L2,T2,d2,e2. L2 ⊢ T0 [d2, e2] ≫ T2 →
-                      (d1 + e1 ≤ d2 ∨ d2 + e2 ≤ d1) →
-                      ∃∃T. L2 ⊢ T1 [d2, e2] ≫ T & L1 ⊢ T2 [d1, e1] ≫ T.
-#L1 #T0 #T1 #d1 #e1 #H elim H -H L1 T0 T1 d1 e1
-[ /2/
-| #L1 #K1 #V1 #T1 #i0 #d1 #e1 #Hd1 #Hde1 #HLK1 #HVT1 #L2 #T2 #d2 #e2 #H1 #H2 
-  elim (tps_inv_lref1 … H1) -H1
-  [ #H destruct -T2 /4/
-  | -HLK1 HVT1 * #K2 #V2 #Hd2 #Hde2 #_ #_ elim H2 -H2 #Hded
-    [ -Hd1 Hde2;
-      lapply (transitive_le … Hded Hd2) -Hded Hd2 #H
-      lapply (lt_to_le_to_lt … Hde1 H) -Hde1 H #H
-      elim (lt_refl_false … H)
-    | -Hd2 Hde1;
-      lapply (transitive_le … Hded Hd1) -Hded Hd1 #H
-      lapply (lt_to_le_to_lt … Hde2 H) -Hde2 H #H
-      elim (lt_refl_false … H)
-    ]
-  ]
-| #L1 #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #L2 #X #d2 #e2 #HX #H
-  elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  elim (IHV01 … HV02 H) -IHV01 HV02 #V #HV1 #HV2
-  elim (IHT01 … HT02 ?) -IHT01 HT02
-  [ -H #T #HT1 #HT2
-    lapply (tps_leq_repl_dx … HT1 (L2. 𝕓{I} V) ?) -HT1 /2/
-    lapply (tps_leq_repl_dx … HT2 (L1. 𝕓{I} V) ?) -HT2 /3 width=5/
-  | -HV1 HV2 >plus_plus_comm_23 >plus_plus_comm_23 in ⊢ (? ? %) elim H -H #H
-    [ @or_introl | @or_intror ] /2 by monotonic_le_plus_l/ (**) (* /3/ is too slow *)
-  ]
-| #L1 #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #L2 #X #d2 #e2 #HX #H
-  elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  elim (IHV01 … HV02 H) -IHV01 HV02;
-  elim (IHT01 … HT02 H) -IHT01 HT02 H /3 width=5/
-]
-qed.
-
-(* Note: the constant 1 comes from tps_subst *)
-(* Basic-1: was: subst1_trans *)
-theorem tps_trans_ge: ∀L,T1,T0,d,e. L ⊢ T1 [d, e] ≫ T0 →
-                      ∀T2. L ⊢ T0 [d, 1] ≫ T2 → 1 ≤ e →
-                      L ⊢ T1 [d, e] ≫ T2.
-#L #T1 #T0 #d #e #H elim H -L T1 T0 d e
-[ #L #I #d #e #T2 #H #He
-  elim (tps_inv_atom1 … H) -H
-  [ #H destruct -T2 //
-  | * #K #V #i #Hd2i #Hide2 #HLK #HVT2 #H destruct -I;
-    lapply (lt_to_le_to_lt … (d + e) Hide2 ?) /2/
-  ]
-| #L #K #V #V2 #i #d #e #Hdi #Hide #HLK #HVW #T2 #HVT2 #He
-  lapply (tps_weak … HVT2 0 (i +1) ? ?) -HVT2 /2/ #HVT2
-  <(tps_inv_lift1_eq … HVT2 … HVW) -HVT2 /2/
-| #L #I #V1 #V0 #T1 #T0 #d #e #_ #_ #IHV10 #IHT10 #X #H #He
-  elim (tps_inv_bind1 … H) -H #V2 #T2 #HV02 #HT02 #H destruct -X;
-  lapply (tps_leq_repl_dx … HT02 (L. 𝕓{I} V0) ?) -HT02 /2/ #HT02
-  lapply (IHT10 … HT02 He) -IHT10 HT02 #HT12
-  lapply (tps_leq_repl_dx … HT12 (L. 𝕓{I} V2) ?) -HT12 /3/
-| #L #I #V1 #V0 #T1 #T0 #d #e #_ #_ #IHV10 #IHT10 #X #H #He
-  elim (tps_inv_flat1 … H) -H #V2 #T2 #HV02 #HT02 #H destruct -X /3/
-]
-qed.
-
-theorem tps_trans_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ≫ T0 →
-                        ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫ T2 → d2 + e2 ≤ d1 →
-                        ∃∃T. L ⊢ T1 [d2, e2] ≫ T & L ⊢ T [d1, e1] ≫ T2.
-#L #T1 #T0 #d1 #e1 #H elim H -L T1 T0 d1 e1
-[ /2/
-| #L #K #V #W #i1 #d1 #e1 #Hdi1 #Hide1 #HLK #HVW #T2 #d2 #e2 #HWT2 #Hde2d1
-  lapply (transitive_le … Hde2d1 Hdi1) -Hde2d1 #Hde2i1
-  lapply (tps_weak … HWT2 0 (i1 + 1) ? ?) -HWT2; normalize /2/ -Hde2i1 #HWT2
-  <(tps_inv_lift1_eq … HWT2 … HVW) -HWT2 /4/
-| #L #I #V1 #V0 #T1 #T0 #d1 #e1 #_ #_ #IHV10 #IHT10 #X #d2 #e2 #HX #de2d1
-  elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  lapply (tps_leq_repl_dx … HT02 (L. 𝕓{I} V0) ?) -HT02 /2/ #HT02
-  elim (IHV10 … HV02 ?) -IHV10 HV02 // #V
-  elim (IHT10 … HT02 ?) -IHT10 HT02 [2: /2/ ] #T #HT1 #HT2
-  lapply (tps_leq_repl_dx … HT1 (L. 𝕓{I} V) ?) -HT1;
-  lapply (tps_leq_repl_dx … HT2 (L. 𝕓{I} V2) ?) -HT2 /3 width=6/
-| #L #I #V1 #V0 #T1 #T0 #d1 #e1 #_ #_ #IHV10 #IHT10 #X #d2 #e2 #HX #de2d1
-  elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  elim (IHV10 … HV02 ?) -IHV10 HV02 //
-  elim (IHT10 … HT02 ?) -IHT10 HT02 // /3 width=6/
-]
-qed.