- main proposition on lsx finally proved!

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lsuby.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lsuby.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lsuby.ma
index f6bab12f81ea23f6ad3a454e862d3370d4d0513f..6c90b202b9a44388297b107b64f8a35f255eb691 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lsuby.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lsuby.ma
@@ -57,7 +57,7 @@ lemma lsuby_refl: ∀L,d,e. L ⊑×[d, e] L.
 #He destruct /2 width=1 by lsuby_zero, lsuby_pair/
 qed.
 
-lemma lsuby_O1: ∀L2,L1,d. |L2| ≤ |L1| → L1 ⊑×[d, yinj 0] L2.
+lemma lsuby_O2: ∀L2,L1,d. |L2| ≤ |L1| → L1 ⊑×[d, yinj 0] L2.
 #L2 elim L2 -L2 // #L2 #I2 #V2 #IHL2 * normalize
 [ #d #H lapply (le_n_O_to_eq … H) -H <plus_n_Sm #H destruct
 | #L1 #I1 #V1 #d #H lapply (le_plus_to_le_r … H) -H #HL12
@@ -69,7 +69,7 @@ qed.
 lemma lsuby_sym: ∀d,e,L1,L2. L1 ⊑×[d, e] L2 → |L1| = |L2| → L2 ⊑×[d, e] L1.
 #d #e #L1 #L2 #H elim H -d -e -L1 -L2
 [ #L1 #d #e #H >(length_inv_zero_dx … H) -L1 //
-| /2 width=1 by lsuby_O1/
+| /2 width=1 by lsuby_O2/
 | #I1 #I2 #L1 #L2 #V #e #_ #IHL12 #H lapply (injective_plus_l … H)
   /3 width=1 by lsuby_pair/
 | #I1 #I2 #L1 #L2 #V1 #V2 #d #e #_ #IHL12 #H lapply (injective_plus_l … H)
@@ -207,10 +207,12 @@ lemma lsuby_fwd_length: ∀L1,L2,d,e. L1 ⊑×[d, e] L2 → |L2| ≤ |L1|.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e normalize /2 width=1 by le_S_S/
 qed-.
 
-lemma lsuby_fwd_ldrop2_be: ∀L1,L2,d,e. L1 ⊑×[d, e] L2 →
-                           ∀I2,K2,W,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓑ{I2}W →
-                           d ≤ i → i < d + e →
-                           ∃∃I1,K1. K1 ⊑×[0, ⫰(d+e-i)] K2 & ⇩[s, 0, i] L1 ≡ K1.ⓑ{I1}W.
+(* Properties on basic slicing **********************************************)
+
+lemma lsuby_ldrop_trans_be: ∀L1,L2,d,e. L1 ⊑×[d, e] L2 →
+                            ∀I2,K2,W,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓑ{I2}W →
+                            d ≤ i → i < d + e →
+                            ∃∃I1,K1. K1 ⊑×[0, ⫰(d+e-i)] K2 & ⇩[s, 0, i] L1 ≡ K1.ⓑ{I1}W.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e
 [ #L1 #d #e #J2 #K2 #W #s #i #H
   elim (ldrop_inv_atom1 … H) -H #H destruct