update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
index e1be5ded0f1eaaac979fcb422bf9fc9b75ecef40..ad0de7230e87c803d0aade06d7b13f53738f9ab3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -14,16 +14,13 @@
 
 include "delayed_updating/substitution/fsubst.ma".
 include "delayed_updating/substitution/lift_prototerm_eq.ma".
-(*
-include "delayed_updating/syntax/preterm.ma".
-include "delayed_updating/syntax/prototerm_proper.ma".
-*)
+
 (* FOCALIZED SUBSTITUTION ***************************************************)
 
 (* Constructions with lift for preterm **************************************)
 
 lemma lift_term_fsubst_sn (f) (t) (u) (p):
-      (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u] ⊆ ↑[f](t[⋔p←u]).
+      (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u] ⊆ 🠡[f](t[⋔p←u]).
 #f #t #u #p #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
   >lift_path_append
@@ -35,7 +32,7 @@ lemma lift_term_fsubst_sn (f) (t) (u) (p):
 qed-.
 
 lemma lift_term_fsubst_dx (f) (t) (u) (p):
-      ↑[f](t[⋔p←u]) ⊆ (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u].
+      🠡[f](t[⋔p←u]) ⊆ (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u].
 #f #t #u #p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
@@ -43,12 +40,12 @@ lemma lift_term_fsubst_dx (f) (t) (u) (p):
   /2 width=3 by ex2_intro/
 | #Hq #H0 #H1 destruct
   @or_intror @conj [ /2 width=1 by in_comp_lift_path_term/ ] -Hq #r #Hr
-  elim (lift_path_inv_append_dx … Hr) -Hr #s1 #s2 #Hs1 #_ #H1 destruct
+  elim (lift_path_inv_append_sn … Hr) -Hr #s1 #s2 #Hs1 #_ #H1 destruct
   lapply (lift_path_inj … Hs1) -Hs1 #H1 destruct 
   /2 width=2 by/
 ]
 qed-.
 
 lemma lift_term_fsubst (f) (t) (u) (p):
-      (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u] ⇔ ↑[f](t[⋔p←u]).
+      (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u] ⇔ 🠡[f](t[⋔p←u]).
 /3 width=1 by lift_term_fsubst_sn, conj, lift_term_fsubst_dx/ qed.