(* *)
(**************************************************************************)
-include "delayed_updating/syntax/path_closed_height.ma".
+include "delayed_updating/syntax/path_closed.ma".
include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
(* CLOSED CONDITION FOR PATH ************************************************)
(* Constructions with structure *********************************************)
-lemma path_closed_structure_height (p) (n):
- p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♯p+n❩.
-#p #n #Hn elim Hn -Hn //
-#p #n #_ #IH [ <nplus_succ_dx ]
+lemma path_closed_structure_depth (p):
+ ⊗p ϵ 𝐂❨♭p❩.
+#p elim p -p // *
/2 width=1 by pcc_L_dx, pcc_A_dx, pcc_S_dx/
qed.
-
-lemma path_closed_structure_depth (p) (n):
- p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♭p❩.
-#p #n #Hp <path_closed_depth
-/2 width=3 by path_closed_structure_height/
-qed.