diff --git a/compiler/src/dotty/tools/dotc/core/TyperState.scala b/compiler/src/dotty/tools/dotc/core/TyperState.scala
index 5274a2beef9d..d562e3d708d8 100644
--- a/compiler/src/dotty/tools/dotc/core/TyperState.scala
+++ b/compiler/src/dotty/tools/dotc/core/TyperState.scala
@@ -80,7 +80,7 @@ class TyperState(private val previous: TyperState /* | Null */) {
   def uninstVars: Seq[TypeVar] = constraint.uninstVars
 
   /** The set of uninstantiated type variables which have this state as their owning state */
-  private[this] var myOwnedVars: TypeVars = SimpleIdentitySet.empty
+  private[this] var myOwnedVars: TypeVars = collection.immutable.Set.empty
   def ownedVars: TypeVars = myOwnedVars
   def ownedVars_=(vs: TypeVars): Unit = myOwnedVars = vs
 
diff --git a/compiler/src/dotty/tools/dotc/core/Types.scala b/compiler/src/dotty/tools/dotc/core/Types.scala
index d403aa1dd183..c469e5e47fe1 100644
--- a/compiler/src/dotty/tools/dotc/core/Types.scala
+++ b/compiler/src/dotty/tools/dotc/core/Types.scala
@@ -3757,7 +3757,7 @@ object Types {
     }
   }
 
-  type TypeVars = SimpleIdentitySet[TypeVar]
+  type TypeVars = collection.immutable.Set[TypeVar]
 
   // ------ MatchType ---------------------------------------------------------------