update in static_2 and app_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / functional / flifts.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/functional/flifts.ma b/matita/matita/contribs/lambdadelta/apps_2/functional/flifts.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ground_2/notation/functions/uparrowstar_2.ma".
+include "apps_2/notation/functional/uparrow_2.ma".
+include "static_2/relocation/lifts.ma".
+
+(* GENERIC FUNCTIONAL RELOCATION ********************************************)
+
+rec definition flifts f U on U ≝ match U with
+[ TAtom I     ⇒ match I with
+  [ Sort _ ⇒ U
+  | LRef i ⇒ #(f@❴i❵)
+  | GRef _ ⇒ U
+  ]
+| TPair I V T ⇒ match I with
+  [ Bind2 p I ⇒ ⓑ{p,I}(flifts f V).(flifts (⫯f) T)
+  | Flat2 I   ⇒ ⓕ{I}(flifts f V).(flifts f T)
+  ]
+].
+
+interpretation "generic functional relocation (term)"
+   'UpArrowStar f T = (flifts f T).
+
+interpretation "uniform functional relocation (term)"
+   'UpArrow i T = (flifts (uni i) T).
+
+(* Main properties **********************************************************)
+
+theorem flifts_lifts: ∀T,f. ⬆*[f]T ≘ ↑*[f]T.
+#T elim T -T *
+/2 width=1 by lifts_sort, lifts_lref, lifts_gref, lifts_bind, lifts_flat/
+qed.
+
+(* Main inversion properties ************************************************)
+
+theorem flifts_inv_lifts: ∀f,T1,T2. ⬆*[f]T1 ≘ T2 → ↑*[f]T1 = T2.
+#f #T1 #T2 #H elim H -f -T1 -T2 //
+[ #f #i1 #i2 #H <(at_inv_total … H) //
+| #f #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT <IHV <IHT -V2 -T2 //
+| #f #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT <IHV <IHT -V2 -T2 //
+]
+qed-.
+
+(* Derived properties *******************************************************)
+
+lemma flifts_lref_uni: ∀l,i. ↑[l](#i) = #(l+i).
+/3 width=1 by flifts_inv_lifts, lifts_lref_uni/ qed.
+(*
+lemma flift_join: ∀e1,e2,T. ⬆[e1, e2] ↑[0, e1] T ≡ ↑[0, e1 + e2] T.
+#e1 #e2 #T
+lapply (flift_lift T 0 (e1+e2)) #H
+elim (lift_split … H e1 e1) -H // #U #H
+>(flift_inv_lift … H) -H //
+qed.
+*)