- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / frees_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
index e43517ff90c04d9008b96de6eabe6e9ac60e4adb..8f683595597b0cbb9edeafb311494d755fb5c4b5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/frees_append.ma
@@ -19,13 +19,13 @@ include "basic_2/multiple/frees.ma".
 
 (* Properties on append for local environments ******************************)
 
-lemma frees_append: ∀L2,U,d,i. L2 ⊢ i ϵ 𝐅*[d]⦃U⦄ → i ≤ |L2| →
-                    ∀L1. L1 @@ L2 ⊢ i ϵ 𝐅*[d]⦃U⦄.
-#L2 #U #d #i #H elim H -L2 -U -d -i /3 width=2 by frees_eq/
-#I #L2 #K2 #U #W #d #i #j #Hdj #Hji #HnU #HLK2 #_ #IHW #Hi #L1
+lemma frees_append: ∀L2,U,l,i. L2 ⊢ i ϵ 𝐅*[l]⦃U⦄ → i ≤ |L2| →
+                    ∀L1. L1 @@ L2 ⊢ i ϵ 𝐅*[l]⦃U⦄.
+#L2 #U #l #i #H elim H -L2 -U -l -i /3 width=2 by frees_eq/
+#I #L2 #K2 #U #W #l #i #j #Hlj #Hji #HnU #HLK2 #_ #IHW #Hi #L1
 lapply (drop_fwd_length_minus2 … HLK2) normalize #H0
 lapply (drop_O1_append_sn_le … HLK2 … L1) -HLK2
-[ -I -L1 -K2 -U -W -d /3 width=3 by lt_to_le, lt_to_le_to_lt/
+[ -I -L1 -K2 -U -W -l /3 width=3 by lt_to_le, lt_to_le_to_lt/
 | #HLK2 @(frees_be … HnU HLK2) // -HnU -HLK2 @IHW -IHW
   >(minus_plus_m_m (|K2|) 1) >H0 -H0 /2 width=1 by monotonic_le_minus_l2/
 ]
@@ -33,20 +33,20 @@ qed.
 
 (* Inversion lemmas on append for local environments ************************)
 
-fact frees_inv_append_aux: ∀L,U,d,i. L ⊢ i ϵ 𝐅*[d]⦃U⦄ → ∀L1,L2. L = L1 @@ L2 →
-                           i ≤ |L2| → L2 ⊢ i ϵ 𝐅*[d]⦃U⦄.
-#L #U #d #i #H elim H -L -U -d -i /3 width=2 by frees_eq/
-#Z #L #Y #U #X #d #i #j #Hdj #Hji #HnU #HLY #_ #IHW #L1 #L2 #H #Hi destruct
-elim (drop_O1_lt (Ⓕ) L2 j) [2: -Z -Y -L1 -X -U -d /2 width=3 by lt_to_le_to_lt/ ]
+fact frees_inv_append_aux: ∀L,U,l,i. L ⊢ i ϵ 𝐅*[l]⦃U⦄ → ∀L1,L2. L = L1 @@ L2 →
+                           i ≤ |L2| → L2 ⊢ i ϵ 𝐅*[l]⦃U⦄.
+#L #U #l #i #H elim H -L -U -l -i /3 width=2 by frees_eq/
+#Z #L #Y #U #X #l #i #j #Hlj #Hji #HnU #HLY #_ #IHW #L1 #L2 #H #Hi destruct
+elim (drop_O1_lt (Ⓕ) L2 j) [2: -Z -Y -L1 -X -U -l /2 width=3 by lt_to_le_to_lt/ ]
 #I #K2 #W #HLK2 lapply (drop_fwd_length_minus2 … HLK2) normalize #H0
 lapply (drop_O1_inv_append1_le … HLY … HLK2) -HLY
-[ -Z -I -Y -K2 -L1 -X -U -W -d /3 width=3 by lt_to_le, lt_to_le_to_lt/
+[ -Z -I -Y -K2 -L1 -X -U -W -l /3 width=3 by lt_to_le, lt_to_le_to_lt/
 | normalize #H destruct
   @(frees_be … HnU HLK2) -HnU -HLK2 // @IHW -IHW //
   >(minus_plus_m_m (|K2|) 1) >H0 -H0 /2 width=1 by monotonic_le_minus_l2/
 ]
 qed-.
 
-lemma frees_inv_append: ∀L1,L2,U,d,i. L1 @@ L2 ⊢ i ϵ 𝐅*[d]⦃U⦄ →
-                        i ≤ |L2| → L2 ⊢ i ϵ 𝐅*[d]⦃U⦄.
+lemma frees_inv_append: ∀L1,L2,U,l,i. L1 @@ L2 ⊢ i ϵ 𝐅*[l]⦃U⦄ →
+                        i ≤ |L2| → L2 ⊢ i ϵ 𝐅*[l]⦃U⦄.
 /2 width=4 by frees_inv_append_aux/ qed-.