- cpr is now defined and the cpr_flat propery is proved! (it did not

[helm.git] / matita / matita / lib / lambda-delta / substitution / leq_defs.ma

diff --git a/matita/matita/lib/lambda-delta/substitution/leq_defs.ma b/matita/matita/lib/lambda-delta/substitution/leq_defs.ma
deleted file mode 100644 (file)
index 3c79815..0000000
--- a/matita/matita/lib/lambda-delta/substitution/leq_defs.ma
+++ /dev/null
@@ -1,60 +0,0 @@
-(*
-    ||M||  This file is part of HELM, an Hypertextual, Electronic
-    ||A||  Library of Mathematics, developed at the Computer Science
-    ||T||  Department of the University of Bologna, Italy.
-    ||I||
-    ||T||
-    ||A||  This file is distributed under the terms of the
-    \   /  GNU General Public License Version 2
-     \ /
-      V_______________________________________________________________ *)
-
-include "lambda-delta/syntax/lenv.ma".
-
-(* LOCAL ENVIRONMENT EQUALITY ***********************************************)
-
-inductive leq: lenv → nat → nat → lenv → Prop ≝
-| leq_sort: ∀d,e. leq (⋆) d e (⋆)
-| leq_comp: ∀L1,L2,I1,I2,V1,V2.
-            leq L1 0 0 L2 → leq (L1. 𝕓{I1} V1) 0 0 (L2. 𝕓{I2} V2)
-| leq_eq:   ∀L1,L2,I,V,e. leq L1 0 e L2 → leq (L1. 𝕓{I} V) 0 (e + 1) (L2.𝕓{I} V)
-| leq_skip: ∀L1,L2,I1,I2,V1,V2,d,e.
-            leq L1 d e L2 → leq (L1. 𝕓{I1} V1) (d + 1) e (L2. 𝕓{I2} V2)
-.
-
-interpretation "local environment equality" 'Eq L1 d e L2 = (leq L1 d e L2).
-
-(* Basic properties *********************************************************)
-
-lemma leq_refl: ∀d,e,L. L [d, e] ≈ L.
-#d elim d -d
-[ #e elim e -e [ #L elim L -L /2/ | #e #IHe #L elim L -L /2/ ]
-| #d #IHd #e #L elim L -L /2/
-]
-qed.
-
-lemma leq_sym: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → L2 [d, e] ≈ L1.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e /2/
-qed.
-
-lemma leq_skip_lt: ∀L1,L2,d,e. leq L1 (d - 1) e L2 → 0 < d →
-                   ∀I1,I2,V1,V2. L1. 𝕓{I1} V1 [d, e] ≈ L2. 𝕓{I2} V2.
-
-#L1 #L2 #d #e #HL12 #Hd >(plus_minus_m_m d 1) /2/ 
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma leq_inv_sort1_aux: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → L1 = ⋆ → L2 = ⋆.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e
-[ //
-| #L1 #L2 #I1 #I2 #V1 #V2 #_ #_ #H destruct
-| #L1 #L2 #I #V #e #_ #_ #H destruct
-| #L1 #L2 #I1 #I2 #V1 #V2 #d #e #_ #_ #H destruct
-qed.
-
-lemma leq_inv_sort1: ∀L2,d,e. ⋆ [d, e] ≈ L2 → L2 = ⋆.
-/2 width=5/ qed.
-
-lemma leq_inv_sort2: ∀L1,d,e. L1 [d, e] ≈ ⋆ → L1 = ⋆.
-/3/ qed.