update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index 0202dc9264c50cf0cc99216fbe0eafe7d9d01edf..6825b13aa3109a7765f5fcb12efe9b0594a5856b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,16 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_pn.ma".
 include "delayed_updating/substitution/lift_eq.ma".
 
-axiom lift_path_after (p) (f1) (f2):
+lemma lift_path_after (p) (f1) (f2):
       ↑[f2]↑[f1]p = ↑[f2∘f1]p.
-(*
-#p @(path_ind_lift … p) -p // [ #n | #n #l #p | #p ] #IH #f1 #f2
-[ <lift_path_d_empty_sn <lift_path_d_empty_sn
-| <lift_path_d_lcons_sn <lift_path_d_lcons_sn
+#p @(path_ind_lift … p) -p // [ #n #l #p | #p ] #IH #f1 #f2
+[ <lift_path_d_lcons_sn <lift_path_d_lcons_sn
+  >(lift_path_eq_repl … (tr_compose_assoc …)) //
 | <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
-*)
+  >tr_compose_push_bi //
+]
+qed.
+
 include "delayed_updating/substitution/lift_prototerm.ma".
 
 axiom lift_term_after (t) (f1) (f2):
@@ -32,7 +36,7 @@ include "delayed_updating/syntax/prototerm_constructors.ma".
 (* LIFT FOR PROTOTERM *******************************************************)
 
 lemma lift_iref_after_sn (f) (t) (n:pnat):
-      ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
+      (↑[f∘𝐮❨n❩]t) ⊆ ↑[f](𝛗n.t).
 #f #t #n #p * #q #Hq #H0 destruct
 @(ex2_intro … (𝗱n◗𝗺◗q))
 /2 width=1 by in_comp_iref/