include "delayed_updating/notation/functions/uparrow_4.ma".
include "delayed_updating/notation/functions/uparrow_2.ma".
include "delayed_updating/syntax/path.ma".
-include "ground/relocation/tr_id_pap.ma".
+include "ground/relocation/tr_uni.ma".
+include "ground/relocation/tr_pap_tls.ma".
(* LIFT FOR PATH ************************************************************)
[ list_empty ⇒ k f (𝐞)
| list_lcons l q ⇒
match l with
- [ label_d n ⇒ lift_gen (A) (λg,p. k g (𝗱(f@⧣❨n❩)◗p)) (𝐢) q
+ [ label_d n ⇒ lift_gen (A) (λg,p. k g (𝗱(f@⧣❨n❩)◗p)) (⇂*[n]f) q
| label_m ⇒ lift_gen (A) (λg,p. k g (𝗺◗p)) f q
| label_L ⇒ lift_gen (A) (λg,p. k g (𝗟◗p)) (⫯f) q
| label_A ⇒ lift_gen (A) (λg,p. k g (𝗔◗p)) f q
// qed.
lemma lift_d_sn (A) (k) (p) (n) (f):
- ↑❨(λg,p. k g (𝗱(f@⧣❨n❩)◗p)), 𝐢, p❩ = ↑{A}❨k, f, 𝗱n◗p❩.
+ ↑❨(λg,p. k g (𝗱(f@⧣❨n❩)◗p)), ⇂*[n]f, p❩ = ↑{A}❨k, f, 𝗱n◗p❩.
// qed.
lemma lift_m_sn (A) (k) (p) (f):
// qed.
lemma lift_rmap_d_sn (f) (p) (n):
- ↑[p]𝐢 = ↑[𝗱n◗p]f.
+ ↑[p](⇂*[ninj n]f) = ↑[𝗱n◗p]f.
// qed.
lemma lift_rmap_m_sn (f) (p):
↑[p]f = ↑[𝗦◗p]f.
// qed.
-(* Advanced cinstructionswith proj_rmap and tr_id ***************************)
-
-lemma lift_rmap_id (p):
- (𝐢) = ↑[p]𝐢.
-#p elim p -p //
-* [ #n ] #p #IH //
-qed.
-
(* Advanced constructions with proj_rmap and path_append ********************)
lemma lift_rmap_append (p2) (p1) (f):
↑[p2]↑[p1]f = ↑[p1●p2]f.
#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
-[ <lift_rmap_d_sn <lift_rmap_d_sn //
-| <lift_rmap_m_sn <lift_rmap_m_sn //
+[ <lift_rmap_m_sn <lift_rmap_m_sn //
| <lift_rmap_A_sn <lift_rmap_A_sn //
| <lift_rmap_S_sn <lift_rmap_S_sn //
]
(* Advanced constructions with proj_rmap and path_rcons *********************)
lemma lift_rmap_d_dx (f) (p) (n):
- (𝐢) = ↑[p◖𝗱n]f.
+ ⇂*[ninj n](↑[p]f) = ↑[p◖𝗱n]f.
// qed.
lemma lift_rmap_m_dx (f) (p):
// qed.
lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
- m = ↑[p◖𝗱n]f@⧣❨m❩.
+ ↑[p]f@⧣❨m+n❩ = ↑[p◖𝗱n]f@⧣❨m❩+↑[p]f@⧣❨n❩.
// qed.