commit by user lroversi

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop.ma
index 7e7ac3c5402105189a651cbc26844198c360c1e8..8782fa93d3257122a743c3e1a3baa354ef22a7ee 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop.ma
@@ -131,6 +131,19 @@ lemma ldrop_inv_skip1: ∀d,e,I,K1,V1,L2. ⇩[d, e] K1. ⓑ{I} V1 ≡ L2 → 0 <
                                 L2 = K2. ⓑ{I} V2.
 /2 width=3/ qed-.
 
+lemma ldrop_inv_O1_pair2: ∀I,K,V,e,L1. ⇩[0, e] L1 ≡ K. ⓑ{I} V →
+                          (e = 0 ∧ L1 = K. ⓑ{I} V) ∨
+                          ∃∃I1,K1,V1. ⇩[0, e - 1] K1 ≡ K. ⓑ{I} V & L1 = K1.ⓑ{I1}V1 & 0 < e.
+#I #K #V #e *
+[ #H lapply (ldrop_inv_atom1 … H) -H #H destruct
+| #L1 #I1 #V1 #H
+  elim (ldrop_inv_O1 … H) -H *
+  [ #H1 #H2 destruct /3 width=1/
+  | /3 width=5/
+  ]
+]
+qed-.
+
 fact ldrop_inv_skip2_aux: ∀d,e,L1,L2. ⇩[d, e] L1 ≡ L2 → 0 < d →
                           ∀I,K2,V2. L2 = K2. ⓑ{I} V2 →
                           ∃∃K1,V1. ⇩[d - 1, e] K1 ≡ K2 &
@@ -186,10 +199,10 @@ lemma ldrop_O1_lt: ∀L,i. i < |L| → ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V.
 ]
 qed.
 
-lemma ldrop_lsubr_ldrop2_abbr: â\88\80L1,L2,d,e. L1 â\89¼ [d, e] L2 →
+lemma ldrop_lsubr_ldrop2_abbr: â\88\80L1,L2,d,e. L1 â\8a\91 [d, e] L2 →
                                ∀K2,V,i. ⇩[0, i] L2 ≡ K2. ⓓV →
                                d ≤ i → i < d + e →
-                               â\88\83â\88\83K1. K1 â\89¼ [0, d + e - i - 1] K2 &
+                               â\88\83â\88\83K1. K1 â\8a\91 [0, d + e - i - 1] K2 &
                                      ⇩[0, i] L1 ≡ K1. ⓓV.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e
 [ #d #e #K1 #V #i #H
@@ -258,11 +271,15 @@ lemma ldrop_fwd_ldrop2: ∀L1,I2,K2,V2,e. ⇩[O, e] L1 ≡ K2. ⓑ{I2} V2 →
 ]
 qed-.
 
+lemma ldrop_fwd_length: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → |L2| ≤ |L1|.
+#L1 #L2 #d #e #H elim H -L1 -L2 -d -e // normalize /2 width=1/
+qed-.
+
 lemma ldrop_fwd_lw: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ♯{L2} ≤ ♯{L1}.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e // normalize
 [ /2 width=3/
 | #L1 #L2 #I #V1 #V2 #d #e #_ #HV21 #IHL12
-  >(tw_lift … HV21) -HV21 /2 width=1/
+  >(lift_fwd_tw … HV21) -HV21 /2 width=1/
 ]
 qed-.