+(**************************************************************************)
+(* ___ *)
+(* ||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 "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/relations/predicate_p_tail_1.ma".
+include "ground/xoa/ex_1_2.ma".
+
+(* PROPER CONDITION FOR PATH ************************************************)
+
+definition ppc: predicate path ≝
+ λp. 𝐞 = p → ⊥
+.
+
+interpretation
+ "proper condition (path)"
+ 'PredicatePTail p = (ppc p).
+
+(* Basic constructions ******************************************************)
+
+lemma ppc_lcons (l) (q): Ꝕ(l◗q).
+#l #p #H destruct
+qed.
+
+(* Basic inversions ********************************************************)
+
+lemma ppc_inv_lcons (p):
+ Ꝕp → ∃∃l,q. l◗q = p.
+*
+[ #H elim H -H //
+| #l #q #_ /2 width=3 by ex1_2_intro/
+]
+qed-.