Definition dist_compl_def_1 (A : Set) (p : prechain A) : Prop :=
  dist_compl_def_0 A p -> forall m : Map A, dist_compl_def_0 A (concat A p m).

Lemma dist_compl_1 : forall (A : Set) (m : Map A), dist_compl_def_1 A (single A m).