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