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_7 : forall (A : Set) (x y : Map A) (z : prechain A), non_dist_chain A (concat A z x) -> ~ dist_chain A (concat A z x) -> ~ dist_chain A (concat A (concat A z x) y).