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_0 :
forall (A : Set) (m : Map A), pre_domok_incr_chain_def A (single A m).