(* Check that Burali-Forti paradox does not go through *)
(* Source: contrib/Rocq/PARADOX/{Logics,BuraliForti},v *)
(* Some properties about relations on objects in Type *)
Inductive ACC (A : Type) (R : A -> A -> Prop) : A -> Prop :=
ACC_intro :
forall x : A, (forall y : A, R y x -> ACC A R y) -> ACC A R x.

Lemma ACC_nonreflexive :
forall (A : Type) (R : A -> A -> Prop) (x : A),
ACC A R x -> R x x -> False.