End StrictTotalOrderViaEquiv.
Section Operators.
Variable A: Type.
Variable R1 R2 eqA: relation A.

(* Specifications: *)
Lemma intersection_Reflexive: Reflexive R1 -> Reflexive R2 -> Reflexive (intersection R1 R2).
Lemma intersection_Symmetric: Symmetric R1 -> Symmetric R2 -> Symmetric (intersection R1 R2).
Lemma intersection_Transitive: Transitive R1 -> Transitive R2 -> Transitive (intersection R1 R2).
Lemma union_IrreflViaEquiv: IrreflViaEquiv R1 eqA -> IrreflViaEquiv R2 eqA -> IrreflViaEquiv (union R1 R2) eqA.
Theorem intersection_Equivalence: Equivalence R1 -> Equivalence R2 -> Equivalence (intersection R1 R2).
End Operators.