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diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
index b3957eaf3..622ee0f55 100644
--- a/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
@@ -17,7 +17,7 @@ include "ground/lib/subset_inclusion.ma".
 
 (* EQUIVALENCE FOR SUBSETS **************************************************)
 
-definition subset_eq (A): relation2 𝒫❨A❩ 𝒫❨A❩ ≝
+definition subset_eq (A): relation2 (𝒫❨A❩) (𝒫❨A❩) ≝
            λu1,u2. ∧∧ u1 ⊆ u2 & u2 ⊆ u1.
 
 interpretation
@@ -56,3 +56,11 @@ theorem subset_eq_trans (A):
 #A #u1 #u2 * #H12 #H21 #u3 * #H23 #H32
 /3 width=5 by subset_le_trans, conj/
 qed-.
+
+theorem subset_eq_canc_sn (A):
+        left_cancellable … (subset_eq A).
+/3 width=3 by subset_eq_trans, subset_eq_sym/ qed-.
+
+theorem subset_eq_canc_dx (A):
+        right_cancellable … (subset_eq A).
+/3 width=3 by subset_eq_trans, subset_eq_sym/ qed-.