update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind / unwind2_path_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
index 71a169dbfdc71f6a4c0710a61e15cbb9bbaa0d93..ac2166a469d4700d0c8571cbfd58527aa3bc83a1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
@@ -13,13 +13,13 @@
 (**************************************************************************)
 
 include "delayed_updating/unwind/unwind2_path_eq.ma".
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_path_prelift.ma".
 
 (* UNWIND FOR PATH **********************************************************)
 
-(* Properties with lift_path ************************************************)
+(* Constructions with lift_path *********************************************)
 
-lemma unwind2_lift_path_after (p) (f1) (f2):
+lemma lift_unwind2_path_after (p) (f1) (f2):
       ↑[f2]▼[f1]p = ▼[f2∘f1]p.
 #p @(path_ind_unwind … p) -p // [ #n | #p ] #IH #f1 #f2
 [ <unwind2_path_d_empty <unwind2_path_d_empty
@@ -28,3 +28,19 @@ lemma unwind2_lift_path_after (p) (f1) (f2):
   >tr_compose_push_bi //
 ]
 qed.
+
+lemma unwind2_path_after_lift (p) (f1) (f2):
+      ▼[f2]↑[f1]p = ▼[f2∘f1]p.
+#p @(path_ind_unwind … p) -p // [ #n #l ] #p #IH #f1 #f2
+[ <lift_path_d_sn <unwind2_path_d_lcons
+  <lift_path_lcons_prelift <unwind2_path_d_lcons >lift_path_lcons_prelift
+  >IH -IH
+  >(unwind2_path_eq_repl … (tr_compose_assoc …))
+  >(unwind2_path_eq_repl … (tr_compose_assoc …))
+  <unwind2_path_after <unwind2_path_after in ⊢ (???%);
+  /3 width=1 by unwind2_path_eq_repl, eq_f/
+| <lift_path_m_sn <unwind2_path_m_sn <unwind2_path_m_sn //
+| <lift_path_L_sn <unwind2_path_L_sn <unwind2_path_L_sn 
+  >tr_compose_push_bi //
+]
+qed.