diff --git a/algebra/subgroup.hlean b/algebra/subgroup.hlean
index 08a1a32..c5d1598 100644
--- a/algebra/subgroup.hlean
+++ b/algebra/subgroup.hlean
@@ -34,11 +34,8 @@ namespace group
     { intros g p, esimp at *, rewrite p, exact one_inv }
   end
 
-  definition is_trivial_subgroup (G : Group) (R : subgroup_rel G) : Prop :=
-  trunctype.mk (Π g : G, R g ↔ trivial_subgroup G g)
-  begin
-    apply pi.is_trunc_pi, intro g, apply is_trunc_prod
-  end
+  definition is_trivial_subgroup (G : Group) (R : subgroup_rel G) : Type :=
+  (Π g : G, R g → g = 1)
 
   definition full_subgroup.{u} (G : Group.{u}) : subgroup_rel.{u 0} G :=
   begin