diff --git a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
index 7ae72bf4317f..9d21925c6a77 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeComparer.scala
@@ -2376,6 +2376,32 @@ class TypeComparer(initctx: Context) extends ConstraintHandling[AbsentContext] w
         def covariantDisjoint(tp1: Type, tp2: Type, tparam: TypeParamInfo): Boolean =
           provablyDisjoint(tp1, tp2) && typeparamCorrespondsToField(tycon1, tparam)
 
+        // In the invariant case, we used a weaker version of disjointness:
+        // we consider types not equal with respect to =:= to be disjoint
+        // (under any context). This is fine because it matches the runtime
+        // semantics of pattern matching. To implement a pattern such as
+        // `case Inv[T] => ...`, one needs a type tag for `T` and the compiler
+        // is used at runtime to check it the scrutinee's type is =:= to `T`.
+        // Note that this is currently a theoretical concern since we Dotty
+        // doesn't have type tags, meaning that users cannot write patterns
+        // that do type tests on higher kinded types.
+        def invariantDisjoint(tp1: Type, tp2: Type, tparam: TypeParamInfo): Boolean =
+          covariantDisjoint(tp1, tp2, tparam) || !isSameType(tp1, tp2) && {
+            // We can only trust a "no" from `isSameType` when both
+            // `tp1` and `tp2` are fully instantiated.
+            def fullyInstantiated(tp: Type): Boolean = new TypeAccumulator[Boolean] {
+              override def apply(x: Boolean, t: Type) =
+                x && {
+                  t match {
+                    case tp: TypeRef if tp.symbol.isAbstractOrParamType => false
+                    case _: SkolemType | _: TypeVar => false
+                    case _ => foldOver(x, t)
+                  }
+                }
+            }.apply(true, tp)
+            fullyInstantiated(tp1) && fullyInstantiated(tp2)
+          }
+
         args1.lazyZip(args2).lazyZip(tycon1.typeParams).exists {
           (arg1, arg2, tparam) =>
             val v = tparam.paramVarianceSign
@@ -2386,21 +2412,7 @@ class TypeComparer(initctx: Context) extends ConstraintHandling[AbsentContext] w
               // instantiated to `Any` belongs to both types.
               false
             else
-              covariantDisjoint(arg1, arg2, tparam) || !isSameType(arg1, arg2) && {
-                // We can only trust a "no" from `isSameType` when both
-                // `arg1` and `arg2` are fully instantiated.
-                def fullyInstantiated(tp: Type): Boolean = new TypeAccumulator[Boolean] {
-                  override def apply(x: Boolean, t: Type) =
-                    x && {
-                      t match {
-                        case tp: TypeRef if tp.symbol.isAbstractOrParamType => false
-                        case _: SkolemType | _: TypeVar => false
-                        case _ => foldOver(x, t)
-                      }
-                    }
-                }.apply(true, tp)
-                fullyInstantiated(arg1) && fullyInstantiated(arg2)
-              }
+              invariantDisjoint(arg1, arg2, tparam)
         }
       case (tp1: HKLambda, tp2: HKLambda) =>
         provablyDisjoint(tp1.resType, tp2.resType)
diff --git a/tests/pos/8778.scala b/tests/pos/8778.scala
new file mode 100644
index 000000000000..c91f765cca01
--- /dev/null
+++ b/tests/pos/8778.scala
@@ -0,0 +1,23 @@
+trait Inv[T]
+
+object Test {
+  type M[X] = X match {
+    case Inv[Int & String] => Int
+      // the type test for Inv[Int & String] cannot be checked at runtime
+      // BUT if it could, ...
+    case Any => String
+  }
+
+  def m[X](x: X): M[X] = x match {
+    case _: Inv[Int & String] => 1
+    case _: Any => "s"
+  }
+
+  // Suppose we somehow manage to convince the compiler of that...
+  val ev: Inv[Nothing] =:= Inv[Int & String] = (implicitly[Int =:= Int]).asInstanceOf
+
+  val invN: Inv[Nothing] = new Inv[Nothing] {}
+  m(invN)     // reduces to Int    both as a value and as a type
+  m(ev(invN)) // reduces to String both as a value and as a type
+}
+