Definition pre_domok_incr_chain_def (A : Set) (p : prechain A) :=
  forall (T : mEnsemble A) (r : mRelation A),
  prechain_dom_ok A T p /\ prechain_incr A r p -> chain A T r p.

Lemma pre_domok_incr_chain_1 : forall (A : Set) (p : prechain A), pre_domok_incr_chain_def A p -> forall m : Map A, pre_domok_incr_chain_def A (concat A p m).