qed.
coercion setoid1_of_setoid.
+prefer coercion Type_OF_setoid.
definition reflexive2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λA:Type2.λR:A→A→CProp2.∀x:A.R x x.
definition symmetric2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λC:Type2.λlt:C→C→CProp2. ∀x,y:C.lt x y → lt y x.
qed.
coercion setoid2_of_setoid1.
+prefer coercion Type_OF_setoid2.
+prefer coercion Type_OF_setoid.
+prefer coercion Type_OF_setoid1.
+(* we prefer 0 < 1 < 2 *)
interpretation "setoid2 eq" 'eq x y = (eq_rel2 _ (eq2 _) x y).
interpretation "setoid1 eq" 'eq x y = (eq_rel1 _ (eq1 _) x y).