#[global]
Hint Resolve same_relation_is_equivalence : core.

(* Specifications: *)
Theorem cong_reflexive_same_relation :
forall (U:Type) (R R':Relation U),
same_relation U R R' -> Reflexive U R -> Reflexive U R'.
Theorem cong_symmetric_same_relation :
forall (U:Type) (R R':Relation U),
same_relation U R R' -> Symmetric U R -> Symmetric U R'.
Theorem cong_antisymmetric_same_relation :
forall (U:Type) (R R':Relation U),
same_relation U R R' -> Antisymmetric U R -> Antisymmetric U R'.
Theorem cong_transitive_same_relation :
forall (U:Type) (R R':Relation U),
same_relation U R R' -> Transitive U R -> Transitive U R'.