diff --git a/lib/inference.ml b/lib/inference.ml
index c620ddc..f06b55c 100644
--- a/lib/inference.ml
+++ b/lib/inference.ml
@@ -22,6 +22,11 @@ let typeof t =
          (match proj with
           | Term.First -> Some ty1, env
           | Term.Second -> Some ty2, env)
+       | Some (Type.Var id), env' ->
+         (* Variable is a product *)
+         (match TypeSubstitution.find id env' with
+          | Some ty -> Some ty, env'
+          | None -> None, env')
        | _ -> None, env)
     | Term.Fun (id, body) ->
       let arg = TypeSubstitution.singleton id (Type.Var id) in