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
new file mode 100644 (file)
index 0000000..e1be5de
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -0,0 +1,54 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+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 #u #p #ql * *
+[ #rl * #r #Hr #H1 #H2 destruct
+  >lift_path_append
+  /4 width=3 by in_comp_lift_path_term, or_introl, ex2_intro/
+| * #q #Hq #H1 #H0
+  @(ex2_intro … H1) @or_intror @conj // -Hq #r #H2 destruct
+  /2 width=2 by/
+]
+qed-.
+
+lemma lift_term_fsubst_dx (f) (t) (u) (p):
+      ↑[f](t[⋔p←u]) ⊆ (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u].
+#f #t #u #p #ql * #q * *
+[ #r #Hu #H1 #H2 destruct
+  @or_introl @ex2_intro
+  [|| <lift_path_append // ]
+  /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
+  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]).
+/3 width=1 by lift_term_fsubst_sn, conj, lift_term_fsubst_dx/ qed.