update in ground, basic_2A and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / substitution / drop_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/substitution/drop_append.ma b/matita/matita/contribs/lambdadelta/basic_2A/substitution/drop_append.ma
index 49d734ceaebd0ccc355ef2a7e7c4b7d993dd86e7..76198fb23a0d09459c653365d1ea7d06498c9b48 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2A/substitution/drop_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2A/substitution/drop_append.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/lib/arith_2a.ma".
 include "basic_2A/grammar/lenv_append.ma".
 include "basic_2A/substitution/drop.ma".
 
@@ -21,19 +22,19 @@ include "basic_2A/substitution/drop.ma".
 
 fact drop_O1_append_sn_le_aux: ∀L1,L2,s,l,m. ⬇[s, l, m] L1 ≡ L2 →
                                l = 0 → m ≤ |L1| →
-                               ∀L. ⬇[s, 0, m] L @@ L1 ≡ L @@ L2.
+                               ∀L. ⬇[s, 0, m] L ● L1 ≡ L ● L2.
 #L1 #L2 #s #l #m #H elim H -L1 -L2 -l -m normalize
 [2,3,4: /4 width=1 by drop_skip_lt, drop_drop, arith_b1, lt_minus_to_plus_r, monotonic_pred/ ]
 #l #m #_ #_ #H <(le_n_O_to_eq … H) -H //
 qed-.
 
 lemma drop_O1_append_sn_le: ∀L1,L2,s,m. ⬇[s, 0, m] L1 ≡ L2 → m ≤ |L1| →
-                            ∀L. ⬇[s, 0, m] L @@ L1 ≡ L @@ L2.
+                            ∀L. ⬇[s, 0, m] L ● L1 ≡ L ● L2.
 /2 width=3 by drop_O1_append_sn_le_aux/ qed.
 
 (* Inversion lemmas on append for local environments ************************)
 
-lemma drop_O1_inv_append1_ge: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 @@ L2 ≡ K →
+lemma drop_O1_inv_append1_ge: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 ● L2 ≡ K →
                               |L2| ≤ m → ⬇[s, 0, m - |L2|] L1 ≡ K.
 #K #L1 #L2 elim L2 -L2 normalize //
 #L2 #I #V #IHL2 #s #m #H #H1m
@@ -44,8 +45,8 @@ elim (drop_inv_O1_pair1 … H) -H * #H2m #HL12 destruct
 ]
 qed-.
 
-lemma drop_O1_inv_append1_le: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 @@ L2 ≡ K → m ≤ |L2| →
-                              ∀K2. ⬇[s, 0, m] L2 ≡ K2 → K = L1 @@ K2.
+lemma drop_O1_inv_append1_le: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 ● L2 ≡ K → m ≤ |L2| →
+                              ∀K2. ⬇[s, 0, m] L2 ≡ K2 → K = L1 ● K2.
 #K #L1 #L2 elim L2 -L2 normalize
 [ #s #m #H1 #H2 #K2 #H3 lapply (le_n_O_to_eq … H2) -H2
   #H2 elim (drop_inv_atom1 … H3) -H3 #H3 #_ destruct