TypeEqualsBool class can assert type inequality.

bower.json

@@ -17,7 +17,6 @@
   ],
   "dependencies": {
     "purescript-proxy": "^2.0.0",
-    "purescript-symbols": "^3.0.0",
-    "purescript-type-equality": "^2.0.0"
+    "purescript-symbols": "^3.0.0"
   }
 }

src/Type/Equality.purs

@@ -0,0 +1,41 @@
+module Type.Equality
+  ( class TypeEquals
+  , to
+  , from
+  , class TypeEqualsBool
+  ) where
+
+import Type.Data.Boolean (kind Boolean, True, False)
+
+-- | This type class asserts that types `a` and `b`
+-- | are equal.
+-- |
+-- | The functional dependencies and the single
+-- | instance below will force the two type arguments
+-- | to unify when either one is known.
+-- |
+-- | Note: any instance will necessarily overlap with
+-- | `refl` below, so instances of this class should
+-- | not be defined in libraries.
+class TypeEquals a b | a -> b, b -> a where
+  to :: a -> b
+  from :: b -> a
+
+instance refl :: TypeEquals a a where
+  to a = a
+  from a = a
+
+-- | This type class asserts that types `a` and `b`
+-- | are or are not equal, depending on the type of `o`.
+-- |
+-- | `o` will be either `True`, if `a` is `b`,
+-- | or `False` otherwise.
+-- |
+-- | When `o` is specified to be `True`/`False` then this type class
+-- | acts as an assertion that `a` and `b` are equal/not equal, respectively.
+-- |
+-- | Instances should not be defined in libraries.
+class TypeEqualsBool a b (o :: Boolean) | a b -> o
+
+instance reflTypeEqualsBool :: TypeEqualsBool a a True
+else instance notTypeEqualsBool :: TypeEqualsBool a b False