#[local] Infix "\in" := E.In.
#[local] Infix "\subseteq" := E.isSubsetOf.
#[local] Obligation Tactic := i.
Create HintDb poset_hints.

Lemma well_founded_implies_Irreflexive {A : Type} (R : A -> A -> Prop)
(WF : well_founded R)
: Irreflexive R.