- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / drop_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma
index 2cb36a8c767ed2fb80feabfb75dd0e33fe66dd87..ee2e49245ce3e5d3e2273a19ff9f261c5b7d925e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma
@@ -19,38 +19,38 @@ include "basic_2/substitution/drop.ma".
 
 (* Properties on append for local environments ******************************)
 
-fact drop_O1_append_sn_le_aux: ∀L1,L2,s,d,e. ⬇[s, d, e] L1 ≡ L2 →
-                               d = 0 → e ≤ |L1| →
-                               ∀L. ⬇[s, 0, e] L @@ L1 ≡ L @@ L2.
-#L1 #L2 #s #d #e #H elim H -L1 -L2 -d -e normalize
+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.
+#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/ ]
-#d #e #_ #_ #H <(le_n_O_to_eq … H) -H //
+#l #m #_ #_ #H <(le_n_O_to_eq … H) -H //
 qed-.
 
-lemma drop_O1_append_sn_le: ∀L1,L2,s,e. ⬇[s, 0, e] L1 ≡ L2 → e ≤ |L1| →
-                            ∀L. ⬇[s, 0, e] L @@ L1 ≡ L @@ L2.
+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.
 /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,e. ⬇[s, 0, e] L1 @@ L2 ≡ K →
-                              |L2| ≤ e → ⬇[s, 0, e - |L2|] L1 ≡ 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 #e #H #H1e
-elim (drop_inv_O1_pair1 … H) -H * #H2e #HL12 destruct
-[ lapply (le_n_O_to_eq … H1e) -H1e -IHL2
+#L2 #I #V #IHL2 #s #m #H #H1m
+elim (drop_inv_O1_pair1 … H) -H * #H2m #HL12 destruct
+[ lapply (le_n_O_to_eq … H1m) -H1m -IHL2
   >commutative_plus normalize #H destruct
 | <minus_plus >minus_minus_comm /3 width=1 by monotonic_pred/
 ]
 qed-.
 
-lemma drop_O1_inv_append1_le: ∀K,L1,L2,s,e. ⬇[s, 0, e] L1 @@ L2 ≡ K → e ≤ |L2| →
-                              ∀K2. ⬇[s, 0, e] 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 #e #H1 #H2 #K2 #H3 lapply (le_n_O_to_eq … H2) -H2
+[ #s #m #H1 #H2 #K2 #H3 lapply (le_n_O_to_eq … H2) -H2
   #H2 elim (drop_inv_atom1 … H3) -H3 #H3 #_ destruct
   >(drop_inv_O2 … H1) -H1 //
-| #L2 #I #V #IHL2 #s #e @(nat_ind_plus … e) -e [ -IHL2 ]
+| #L2 #I #V #IHL2 #s #m @(nat_ind_plus … m) -m [ -IHL2 ]
   [ #H1 #_ #K2 #H2
     lapply (drop_inv_O2 … H1) -H1 #H1
     lapply (drop_inv_O2 … H2) -H2 #H2 destruct //