(* *)
(**************************************************************************)
-include "ground_2/notation/functions/uparrowstar_2.ma".
+include "ground/notation/functions/uparrowstar_2.ma".
include "apps_2/notation/functional/uparrow_2.ma".
include "static_2/relocation/lifts.ma".
rec definition flifts f U on U ≝ match U with
[ TAtom I ⇒ match I with
[ Sort _ ⇒ U
- | LRef i ⇒ #(f@❴i❵)
+ | 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)
+ [ Bind2 p I ⇒ ⓑ[p,I](flifts f V).(flifts (⫯f) T)
+ | Flat2 I ⇒ ⓕ[I](flifts f V).(flifts f T)
]
].
(* Basic properties *********************************************************)
-lemma flifts_lref (f) (i): ↑*[f](#i) = #(f@❴i❵).
+lemma flifts_lref (f) (i): ↑*[f](#i) = #(f@⧣❨i❩).
// qed.
-lemma flifts_bind (f) (p) (I) (V) (T): ↑*[f](ⓑ{p,I}V.T) = ⓑ{p,I}↑*[f]V.↑*[⫯f]T.
+lemma flifts_bind (f) (p) (I) (V) (T): ↑*[f](ⓑ[p,I]V.T) = ⓑ[p,I]↑*[f]V.↑*[⫯f]T.
// qed.
-lemma flifts_flat (f) (I) (V) (T): ↑*[f](ⓕ{I}V.T) = ⓕ{I}↑*[f]V.↑*[f]T.
+lemma flifts_flat (f) (I) (V) (T): ↑*[f](ⓕ[I]V.T) = ⓕ[I]↑*[f]V.↑*[f]T.
// qed.
(* Main properties **********************************************************)
-theorem flifts_lifts: â\88\80T,f. â¬\86*[f]T ≘ ↑*[f]T.
+theorem flifts_lifts: â\88\80T,f. â\87§*[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: â\88\80f,T1,T2. â¬\86*[f]T1 ≘ T2 → ↑*[f]T1 = T2.
+theorem flifts_inv_lifts: â\88\80f,T1,T2. â\87§*[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 //