- revision of ground_2 and 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 ee2e49245ce3e5d3e2273a19ff9f261c5b7d925e..2ea5033388208dcaf3f1da1fef664266dd6aab35 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_append.ma
@@ -20,32 +20,33 @@ include "basic_2/substitution/drop.ma".
 (* Properties on append for local environments ******************************)
 
 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/ ]
-#l #m #_ #_ #H <(le_n_O_to_eq … H) -H //
+                               l = yinj 0 → m ≤ |L1| →
+                               ∀L. ⬇[s, yinj 0, m] L @@ L1 ≡ L @@ L2.
+#L1 #L2 #s #l #m #H elim H -L1 -L2 -l -m //
+[ #l #m #_ #_ #H <(le_n_O_to_eq … H) -H //
+| normalize /4 width=1 by drop_drop, monotonic_pred/
+| #I #L1 #L2 #V1 #V2 #l #m #_ #_ #_ #H elim (ysucc_inv_O_dx … 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.
+lemma drop_O1_append_sn_le: ∀L1,L2,s,m. ⬇[s, yinj 0, m] L1 ≡ L2 → m ≤ |L1| →
+                            ∀L. ⬇[s, yinj 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 →
-                              |L2| ≤ m → ⬇[s, 0, m - |L2|] L1 ≡ K.
+lemma drop_O1_inv_append1_ge: ∀K,L1,L2,s,m. ⬇[s, yinj 0, m] L1 @@ L2 ≡ K →
+                              |L2| ≤ m → ⬇[s, yinj 0, m - |L2|] L1 ≡ K.
 #K #L1 #L2 elim L2 -L2 normalize //
 #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
+[ lapply (le_n_O_to_eq … H1m) -H1m -IHL2 <plus_n_Sm #H destruct
 | <minus_plus >minus_minus_comm /3 width=1 by monotonic_pred/
 ]
 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, yinj 0, m] L1 @@ L2 ≡ K → m ≤ |L2| →
+                              ∀K2. ⬇[s, yinj 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