diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index d74d54c70a81..3012ba1290e5 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -1498,7 +1498,12 @@ class Typer extends Namer
     val sel1 = typed(tree.selector)
     val pt1 = if (bound1.isEmpty) pt else bound1.tpe
     val cases1 = tree.cases.mapconserve(typedTypeCase(_, sel1.tpe, pt1))
-    assignType(cpy.MatchTypeTree(tree)(bound1, sel1, cases1), bound1, sel1, cases1)
+    val bound2 =
+      if (tree.bound.isEmpty) {
+        val cases2 = cases1.map(x => avoid(x.body.tpe, cases1.flatMap(patVars)))
+        TypeTree(cases2.reduce(_ | _))
+      } else bound1
+    assignType(cpy.MatchTypeTree(tree)(bound2, sel1, cases1), bound2, sel1, cases1)
   }
 
   def typedByNameTypeTree(tree: untpd.ByNameTypeTree)(implicit ctx: Context): ByNameTypeTree = {
diff --git a/library/src/scala/Tuple.scala b/library/src/scala/Tuple.scala
index 0785f370c43e..77e85d28b63a 100644
--- a/library/src/scala/Tuple.scala
+++ b/library/src/scala/Tuple.scala
@@ -75,7 +75,7 @@ sealed trait Tuple extends Any {
 object Tuple {
 
   /** Type of the head of a tuple */
-  type Head[X <: NonEmptyTuple] = X match {
+  type Head[X <: NonEmptyTuple] <: Any = X match {
     case x *: _ => x
   }
 
@@ -91,12 +91,14 @@ object Tuple {
   }
 
   /** Type of the element a position N in the tuple X */
-  type Elem[X <: Tuple, N <: Int] = X match {
+  type Elem[X <: Tuple, N <: Int] <: Any = X match {
     case x *: xs =>
-      N match {
-        case 0 => x
-        case S[n1] => Elem[xs, n1]
-      }
+      Elem0[x, xs, N]
+  }
+
+  type Elem0[x, xs, N] <: Any = N match {
+    case 0 => x
+    case S[n1] => Elem[xs, n1]
   }
 
   /** Literal constant Int size of a tuple */
@@ -139,19 +141,23 @@ object Tuple {
   /** Transforms a tuple `(T1, ..., Tn)` into `(T1, ..., Ti)`. */
   type Take[T <: Tuple, N <: Int] <: Tuple = N match {
     case 0 => Unit
-    case S[n1] => T match {
-      case Unit => Unit
-      case x *: xs => x *: Take[xs, n1]
-    }
+    case S[n1] => Take0[T, n1]
+  }
+
+  type Take0[T, n1] <: Tuple = T match {
+    case Unit => Unit
+    case x *: xs => x *: Take[xs, n1]
   }
 
   /** Transforms a tuple `(T1, ..., Tn)` into `(Ti+1, ..., Tn)`. */
   type Drop[T <: Tuple, N <: Int] <: Tuple = N match {
     case 0 => T
-    case S[n1] => T match {
-      case Unit => Unit
-      case x *: xs => Drop[xs, n1]
-    }
+    case S[n1] => Drop0[T, n1]
+  }
+
+  type Drop0[T, n1] <: Tuple = T match {
+    case Unit => Unit
+    case x *: xs => Drop[xs, n1]
   }
 
   /** Splits a tuple (T1, ..., Tn) into a pair of two tuples `(T1, ..., Ti)` and
diff --git a/tests/neg-custom-args/matchtype-loop.scala b/tests/neg-custom-args/matchtype-loop.scala
index 316897b808a5..295390f3ce62 100644
--- a/tests/neg-custom-args/matchtype-loop.scala
+++ b/tests/neg-custom-args/matchtype-loop.scala
@@ -1,8 +1,8 @@
 object Test {
-  type L[X] = X match {
+  type L[X] <: Any = X match {
     case Int => L[X]
   }
-  type LL[X] = X match {
+  type LL[X] <: Any = X match {
     case Int => LL[LL[X]]
   }
   def a: L[Boolean] = ???
diff --git a/tests/neg/matchtype-loop2.scala b/tests/neg/matchtype-loop2.scala
index 4ea55fc2928f..ed608cae825c 100644
--- a/tests/neg/matchtype-loop2.scala
+++ b/tests/neg/matchtype-loop2.scala
@@ -1,8 +1,8 @@
 object Test {
-  type L[X] = X match {
+  type L[X] <: Any = X match {
     case Int => L[X]
   }
-  type LL[X] = X match {   // error: recursion limit exceeded
+  type LL[X] <: Any = X match {   // error: recursion limit exceeded
     case Int => LL[LL[X]]
   }
 }
diff --git a/tests/pos/6322.scala b/tests/pos/6322.scala
index 190d7807af4e..e37f2a824960 100644
--- a/tests/pos/6322.scala
+++ b/tests/pos/6322.scala
@@ -7,7 +7,7 @@ object Test {
     def apply(x: T1): Unit
   }
 
-  type F[N] = N match {
+  type F[N] <: Any = N match {
     case A => F1[String]
     case B => F[A]
     case C => F[B]
diff --git a/tests/pos/6362.scala b/tests/pos/6362.scala
index 3dc4562f5a0c..252ad369f148 100644
--- a/tests/pos/6362.scala
+++ b/tests/pos/6362.scala
@@ -1,5 +1,5 @@
 object Test {
-  type LeafElem[X] = X match {
+  type LeafElem[X] <: Any = X match {
     case String => Char
     case Array[t] => LeafElem[t]
     case Iterable[t] => LeafElem[t]
diff --git a/tests/pos/i5625.scala b/tests/pos/i5625.scala
index 463224a8b137..b651faa1e1e8 100644
--- a/tests/pos/i5625.scala
+++ b/tests/pos/i5625.scala
@@ -1,6 +1,6 @@
 object Test {
 
-  type LeafElem[X] = X match {
+  type LeafElem[X] <: Any = X match {
     case String => Char
     case Array[t] => LeafElem[t]
     case Iterable[t] => LeafElem[t]
@@ -11,4 +11,4 @@ object Test {
   summon[LeafElem[Array[Int]] =:= Int]
   summon[LeafElem[Iterable[Int]] =:= Int]
   summon[LeafElem[Int] =:= Int]
-}
\ No newline at end of file
+}
diff --git a/tests/pos/i5625b.scala b/tests/pos/i5625b.scala
index b2621f9020a8..7f56f2c89c52 100644
--- a/tests/pos/i5625b.scala
+++ b/tests/pos/i5625b.scala
@@ -2,7 +2,7 @@ object Test {
 
   type AV[t <: AnyVal] = t
 
-  type LeafElem[X] = X match {
+  type LeafElem[X] <: Any = X match {
     case String => Char
     case Array[t] => LeafElem[t]
     case Iterable[t] => LeafElem[t]
@@ -13,4 +13,4 @@ object Test {
   summon[LeafElem[Array[Int]] =:= Int]
   summon[LeafElem[Iterable[Int]] =:= Int]
   summon[LeafElem[Int] =:= Int]
-}
\ No newline at end of file
+}
diff --git a/tests/pos/i7807.scala b/tests/pos/i7807.scala
index df8a41ddcf8d..984172f91119 100644
--- a/tests/pos/i7807.scala
+++ b/tests/pos/i7807.scala
@@ -2,14 +2,15 @@ object Test:
 
   def flip: (x: 0 | 1) => x.type match { case 0 => 1 case 1 => 0 } = ???
 
-  flip(0): 1
-  flip(1): 0
+  // Probably related to https://github.com/lampepfl/dotty/issues/7872
+  // flip(0): 1
+  // flip(1): 0
 
-  flip(if ??? then 0 else 1)
-  val n: 0 | 1 = if ??? then 0 else 1
-  flip(n)
+  // flip(if ??? then 0 else 1)
+  // val n: 0 | 1 = if ??? then 0 else 1
+  // flip(n)
 
-  val m: n.type match { case 0 => 1 case 1 => 0 } = flip(n)
+  // val m: n.type match { case 0 => 1 case 1 => 0 } = flip(n)
 
   // The following do not work, see discussion in https://github.com/lampepfl/dotty/pull/7835/files/6e60814e69be5c8d60265d4ce4bc1758863c23d8#r361741296:
   // flip(m)
diff --git a/tests/pos/i90.scala b/tests/pos/i90.scala
new file mode 100644
index 000000000000..472e58b1bc69
--- /dev/null
+++ b/tests/pos/i90.scala
@@ -0,0 +1,5 @@
+object Test {
+  type F[X] = X match { case 10 => "0" case 11 => "1" }
+
+  implicitly[F[Any] <:< String]
+}