assumption.
qed.
+(*
+
definition powerset_setoid: setoid → setoid1.
intros (T);
constructor 1;
interpretation "subseteq" 'subseteq U V = (fun1 ___ (subseteq _) U V).
+theorem subseteq_refl: ∀A.∀S:Ω \sup A.S ⊆ S.
+ intros 4; assumption.
+qed.
+
+theorem subseteq_trans: ∀A.∀S1,S2,S3: Ω \sup A. S1 ⊆ S2 → S2 ⊆ S3 → S1 ⊆ S3.
+ intros; apply transitive_subseteq_operator; [apply S2] assumption.
+qed.
+
definition overlaps: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
intros;
constructor 1;
[ apply a |4: apply a'] try assumption; apply sym; assumption]
qed.
-interpretation "singleton" 'singl a = (fun_1 __ (singleton _) a).
\ No newline at end of file
+interpretation "singleton" 'singl a = (fun_1 __ (singleton _) a).
+
+*)
\ No newline at end of file