include "ground/arith/nat_plus.ma".
include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/functions/hash_1.ma".
+include "delayed_updating/notation/functions/sharp_1.ma".
(* HEIGHT FOR PATH **********************************************************)
interpretation
"height (path)"
- 'Hash p = (height p).
+ 'Sharp p = (height p).
(* Basic constructions ******************************************************)
-lemma height_empty: ð\9d\9f\8e = ⧣𝐞.
+lemma height_empty: ð\9d\9f\8e = â\99¯𝐞.
// qed.
-lemma height_d_sn (q) (n): ninj n+⧣q = ⧣(𝗱n◗q).
+lemma height_d_sn (q) (n): ninj n+â\99¯q = â\99¯(𝗱n◗q).
// qed.
-lemma height_m_sn (q): ⧣q = ⧣(𝗺◗q).
+lemma height_m_sn (q): â\99¯q = â\99¯(𝗺◗q).
// qed.
-lemma height_L_sn (q): ⧣q = ⧣(𝗟◗q).
+lemma height_L_sn (q): â\99¯q = â\99¯(𝗟◗q).
// qed.
-lemma height_A_sn (q): ⧣q = ⧣(𝗔◗q).
+lemma height_A_sn (q): â\99¯q = â\99¯(𝗔◗q).
// qed.
-lemma height_S_sn (q): ⧣q = ⧣(𝗦◗q).
+lemma height_S_sn (q): â\99¯q = â\99¯(𝗦◗q).
// qed.
(* Main constructions *******************************************************)
theorem height_append (p1) (p2):
- (⧣p2+⧣p1) = ⧣(p1●p2).
+ (â\99¯p2+â\99¯p1) = â\99¯(p1●p2).
#p1 elim p1 -p1 //
* [ #n ] #p1 #IH #p2 <list_append_lcons_sn
[ <height_d_sn <height_d_sn //
(* Constructions with list_rcons ********************************************)
lemma height_d_dx (p) (n):
- (⧣p)+(ninj n) = ⧣(p◖𝗱n).
+ (â\99¯p)+(ninj n) = â\99¯(p◖𝗱n).
// qed.
lemma height_m_dx (p):
- (⧣p) = ⧣(p◖𝗺).
+ (â\99¯p) = â\99¯(p◖𝗺).
// qed.
lemma height_L_dx (p):
- (⧣p) = ⧣(p◖𝗟).
+ (â\99¯p) = â\99¯(p◖𝗟).
// qed.
lemma height_A_dx (p):
- (⧣p) = ⧣(p◖𝗔).
+ (â\99¯p) = â\99¯(p◖𝗔).
// qed.
lemma height_S_dx (p):
- (⧣p) = ⧣(p◖𝗦).
+ (â\99¯p) = â\99¯(p◖𝗦).
// qed.