- advances on hereditarily free variables: now "frees" is primitive

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops_ldrop.ma
index 9712e3277c82c70ba8e18909fa1c1a825b978be5..302829e62b28d7b5a8620db076fe0e00d17b9d7c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops_ldrop.ma
@@ -15,21 +15,22 @@
 include "basic_2/relocation/ldrop_ldrop.ma".
 include "basic_2/substitution/ldrops.ma".
 
-(* GENERIC LOCAL ENVIRONMENT SLICING ****************************************)
+(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
 
 (* Properties concerning basic local environment slicing ********************)
 
-lemma ldrops_ldrop_trans: ∀L1,L,des. ⇩*[des] L1 ≡ L → ∀L2,i. ⇩[0, i] L ≡ L2 →
-                          ∃∃L0,des0,i0. ⇩[0, i0] L1 ≡ L0 & ⇩*[des0] L0 ≡ L2 &
+lemma ldrops_ldrop_trans: ∀L1,L,des. ⇩*[Ⓕ, des] L1 ≡ L → ∀L2,i. ⇩[i] L ≡ L2 →
+                          ∃∃L0,des0,i0. ⇩[i0] L1 ≡ L0 & ⇩*[Ⓕ, des0] L0 ≡ L2 &
                                         @⦃i, des⦄ ≡ i0 & des ▭ i ≡ des0.
 #L1 #L #des #H elim H -L1 -L -des
-[ /2 width=7/
-| #L1 #L3 #L #des3 #d #e #_ #HL3 #IHL13 #L2 #i #HL2
+[ /2 width=7 by ldrops_nil, minuss_nil, at_nil, ex4_3_intro/
+| #L1 #L0 #L #des #d #e #_ #HL0 #IHL0 #L2 #i #HL2
   elim (lt_or_ge i d) #Hid
-  [ elim (ldrop_trans_le … HL3 … HL2 ?) -L /2 width=2/ #L #HL3 #HL2
-    elim (IHL13 … HL3) -L3 /3 width=7/
-  | lapply (ldrop_trans_ge … HL3 … HL2 ?) -L // #HL32
-    elim (IHL13 … HL32) -L3 /3 width=7/
+  [ elim (ldrop_trans_le … HL0 … HL2) -L /2 width=2 by lt_to_le/
+    #L #HL0 #HL2 elim (IHL0 … HL0) -L0 /3 width=7 by ldrops_cons, minuss_lt, at_lt, ex4_3_intro/
+  | lapply (ldrop_trans_ge … HL0 … HL2 ?) -L // #HL02
+    elim (IHL0 … HL02) -L0 /3 width=7 by minuss_ge, at_ge, ex4_3_intro/
   ]
 ]
 qed-.
+