diff --git a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
index 9a6ee7296239..302ad7987889 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
@@ -2857,6 +2857,13 @@ class TypeComparer(@constructorOnly initctx: Context) extends ConstraintHandling
         tp
       case tp: HKTypeLambda =>
         tp
+      case tp: ParamRef =>
+        val st = tp.superTypeNormalized
+        if st.exists then
+          disjointnessBoundary(st)
+        else
+          // workaround for when ParamRef#underlying returns NoType
+          defn.AnyType
       case tp: TypeProxy =>
         disjointnessBoundary(tp.superTypeNormalized)
       case tp: WildcardType =>
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index 9ef075f95e3a..b1bb5805bdc4 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -2375,7 +2375,15 @@ class Typer(@constructorOnly nestingLevel: Int = 0) extends Namer
       report.error(MatchTypeScrutineeCannotBeHigherKinded(sel1Tpe), sel1.srcPos)
     val pt1 = if (bound1.isEmpty) pt else bound1.tpe
     val cases1 = tree.cases.mapconserve(typedTypeCase(_, sel1Tpe, pt1))
-    assignType(cpy.MatchTypeTree(tree)(bound1, sel1, cases1), bound1, sel1, cases1)
+    val bound2 = if tree.bound.isEmpty then
+      val lub = cases1.foldLeft(defn.NothingType: Type): (acc, case1) =>
+        if !acc.exists then NoType
+        else if case1.body.tpe.isProvisional then NoType
+        else acc | case1.body.tpe
+      if lub.exists then TypeTree(lub, inferred = true)
+      else bound1
+    else bound1
+    assignType(cpy.MatchTypeTree(tree)(bound2, sel1, cases1), bound2, sel1, cases1)
   }
 
   def typedByNameTypeTree(tree: untpd.ByNameTypeTree)(using Context): ByNameTypeTree = tree.result match
diff --git a/tests/pos/13633.scala b/tests/pos/13633.scala
index ca0f7e68e81e..8883ef98d0be 100644
--- a/tests/pos/13633.scala
+++ b/tests/pos/13633.scala
@@ -21,7 +21,7 @@ object Sums extends App:
 
   type Reverse[A] = ReverseLoop[A, EmptyTuple]
 
-  type PlusTri[A, B, C]                             = (A, B, C) match
+  type PlusTri[A, B, C] <: Tuple                    = (A, B, C) match
     case (false, false, false)                                              => (false, false)
     case (true, false, false) | (false, true, false) | (false, false, true) => (false, true)
     case (true, true, false) | (true, false, true) | (false, true, true)    => (true, false)
diff --git a/tests/pos/Tuple.Drop.scala b/tests/pos/Tuple.Drop.scala
new file mode 100644
index 000000000000..9b88cc227966
--- /dev/null
+++ b/tests/pos/Tuple.Drop.scala
@@ -0,0 +1,7 @@
+import compiletime.ops.int.*
+
+type Drop[T <: Tuple, N <: Int] <: Tuple = N match
+  case 0 => T
+  case S[n1] => T match
+    case EmptyTuple => EmptyTuple
+    case x *: xs => Drop[xs, n1]
diff --git a/tests/pos/Tuple.Elem.scala b/tests/pos/Tuple.Elem.scala
new file mode 100644
index 000000000000..81494485c321
--- /dev/null
+++ b/tests/pos/Tuple.Elem.scala
@@ -0,0 +1,7 @@
+import compiletime.ops.int.*
+
+type Elem[T <: Tuple, I <: Int] = T match
+  case h *: tail =>
+    I match
+      case 0 => h
+      case S[j] => Elem[tail, j]
diff --git a/tests/pos/i19710.scala b/tests/pos/i19710.scala
new file mode 100644
index 000000000000..03fd1e2d80b3
--- /dev/null
+++ b/tests/pos/i19710.scala
@@ -0,0 +1,11 @@
+import scala.util.NotGiven
+
+type HasName1 = [n] =>> [x] =>> x match {
+    case n => true
+    case _ => false
+  }
+@main def Test = {
+  summon[HasName1["foo"]["foo"] =:= true]
+  summon[NotGiven[HasName1["foo"]["bar"] =:= true]]
+  summon[Tuple.Filter[(1, "foo", 2, "bar"), HasName1["foo"]] =:= Tuple1["foo"]] // error
+}
diff --git a/tests/run-macros/type-show/Test_2.scala b/tests/run-macros/type-show/Test_2.scala
index ace303a6596e..de845f3e84dd 100644
--- a/tests/run-macros/type-show/Test_2.scala
+++ b/tests/run-macros/type-show/Test_2.scala
@@ -1,18 +1,34 @@
 
 object Test {
   import TypeToolbox.*
+
+  def assertEql[A](obt: A, exp: A): Unit =
+    assert(obt == exp, s"\nexpected: $exp\nobtained: $obt")
+
   def main(args: Array[String]): Unit = {
     val x = 5
-    assert(show[x.type] == "x.type")
-    assert(show[Nil.type] == "scala.Nil.type")
-    assert(show[Int] == "scala.Int")
-    assert(show[Int => Int] == "scala.Function1[scala.Int, scala.Int]")
-    assert(show[(Int, String)] == "scala.Tuple2[scala.Int, scala.Predef.String]")
-    assert(show[[X] =>> X match { case Int => Int }] ==
+    assertEql(show[x.type], "x.type")
+    assertEql(show[Nil.type], "scala.Nil.type")
+    assertEql(show[Int], "scala.Int")
+    assertEql(show[Int => Int], "scala.Function1[scala.Int, scala.Int]")
+    assertEql(show[(Int, String)], "scala.Tuple2[scala.Int, scala.Predef.String]")
+    assertEql(show[[X] =>> X match { case Int => Int }],
       """[X >: scala.Nothing <: scala.Any] =>> X match  {
         |  case scala.Int => scala.Int
         |}""".stripMargin)
-    assert(showStructure[[X] =>> X match { case Int => Int }] == """TypeLambda(List(X), List(TypeBounds(TypeRef(ThisType(TypeRef(NoPrefix(), "scala")), "Nothing"), TypeRef(ThisType(TypeRef(NoPrefix(), "scala")), "Any"))), MatchType(TypeRef(ThisType(TypeRef(NoPrefix(), "scala")), "Any"), ParamRef(binder, 0), List(MatchCase(TypeRef(TermRef(ThisType(TypeRef(NoPrefix(), "<root>")), "scala"), "Int"), TypeRef(TermRef(ThisType(TypeRef(NoPrefix(), "<root>")), "scala"), "Int")))))""")
+    assertEql(showStructure[[X] =>> X match { case Int => Int }],
+      """TypeLambda("""+
+        """List(X), """+
+        """List(TypeBounds("""+
+        """TypeRef(ThisType(TypeRef(NoPrefix(), "scala")), "Nothing"), """+
+        """TypeRef(ThisType(TypeRef(NoPrefix(), "scala")), "Any"))), """+
+        """MatchType("""+
+        """TypeRef(TermRef(ThisType(TypeRef(NoPrefix(), "<root>")), "scala"), "Int"), """+ // match type bound
+        """ParamRef(binder, 0), """+
+        """List("""+
+        """MatchCase("""+
+        """TypeRef(TermRef(ThisType(TypeRef(NoPrefix(), "<root>")), "scala"), "Int"), """+
+        """TypeRef(TermRef(ThisType(TypeRef(NoPrefix(), "<root>")), "scala"), "Int")))))""")
 
     // TODO: more complex types:
     //  - implicit function types