1 files changed, 21 insertions, 0 deletions
diff --git a/src/CHAD/Lemmas.hs b/src/CHAD/Lemmas.hs
new file mode 100644
index 0000000..55ef042
--- /dev/null
+++ b/src/CHAD/Lemmas.hs
@@ -0,0 +1,21 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+
+{-# LANGUAGE AllowAmbiguousTypes #-}
+module CHAD.Lemmas (module CHAD.Lemmas, (:~:)(Refl)) where
+
+import Data.Type.Equality
+import Unsafe.Coerce (unsafeCoerce)
+
+
+type family Append a b where
+  Append '[] l = l
+  Append (x : xs) l = x : Append xs l
+
+lemAppendNil :: Append a '[] :~: a
+lemAppendNil = unsafeCoerce Refl
+
+lemAppendAssoc :: Append a (Append b c) :~: Append (Append a b) c
+lemAppendAssoc = unsafeCoerce Refl