- a caracterization of the top elements of the local evironment

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / ldrop.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
index 73a9ff92e373fc9bb0d3aee04849989b25191576..9ab903f1e48055d3f85ef41473ceb6b9e8d8de54 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
@@ -13,8 +13,8 @@
 (**************************************************************************)
 
 include "basic_2/grammar/cl_weight.ma".
-include "basic_2/grammar/lsubs.ma".
 include "basic_2/substitution/lift.ma".
+include "basic_2/substitution/lsubs.ma".
 
 (* LOCAL ENVIRONMENT SLICING ************************************************)
 
@@ -76,6 +76,12 @@ lemma ldrop_inv_O1: ∀e,K,I,V,L2. ⇩[0, e] K. ⓑ{I} V ≡ L2 →
                     (0 < e ∧ ⇩[0, e - 1] K ≡ L2).
 /2 width=3/ qed-.
 
+lemma ldrop_inv_pair1: ∀K,I,V,L2. ⇩[0, 0] K. ⓑ{I} V ≡ L2 → L2 = K. ⓑ{I} V.
+#K #I #V #L2 #H
+elim (ldrop_inv_O1 … H) -H * // #H destruct
+elim (lt_refl_false … H)
+qed-.
+
 (* Basic_1: was: drop_gen_drop *)
 lemma ldrop_inv_ldrop1: ∀e,K,I,V,L2.
                         ⇩[0, e] K. ⓑ{I} V ≡ L2 → 0 < e → ⇩[0, e - 1] K ≡ L2.
@@ -144,10 +150,10 @@ lemma ldrop_O1: ∀L,i. i < |L| → ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V.
 ]
 qed.   
 
-lemma ldrop_lsubs_ldrop1_abbr: ∀L1,L2,d,e. L1 [d, e] ≼ L2 →
+lemma ldrop_lsubs_ldrop1_abbr: ∀L1,L2,d,e. L1 ≼ [d, e] L2 →
                                ∀K1,V,i. ⇩[0, i] L1 ≡ K1. ⓓV →
                                d ≤ i → i < d + e →
-                               ∃∃K2. K1 [0, d + e - i - 1] ≼ K2 &
+                               ∃∃K2. K1 ≼ [0, d + e - i - 1] K2 &
                                      ⇩[0, i] L2 ≡ K2. ⓓV.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e
 [ #d #e #K1 #V #i #H