Load prototheticv5.
Require Export Coq.Classes.RelationClasses.
Require Export Relation_Definitions.
Module Type Mereology (dolce:DOLCE_root)(proto:Protothetic dolce).
Set Typeclasses Axioms Are Instances.
(* ====================== ONTOLOGICAL AXIOM  ============================= *)
Parameter epsilon : relation N.
(* no typing on singulars and plurals *)
Notation "A 'ε' b" := (epsilon A b)  (at level 40).

(* Specifications: *)
Axiom isEpsilon : forall A a, A ε a ≡≡ ((¬forall B, ¬(B ε A)) ∧
(forall C D, ((C ε A) ∧ (D ε A)) ⊃ (C ε D)) ∧
(forall C, (C ε A) ⊃ (C ε a))).