Goal:
  
  A : Type
  P : tree A -> Type
  empty : P Empty
  node : forall l : tree A,
         P l ->
         forall (o : option A) (r : tree A),
         P r -> not_trivially_empty l o r -> P (Node l o r)
  x : A
  ============================
   True


DEBUG:Going to execute:
match goal with
           | |- well_founded _ => auto with *
           | |- ?T => match type of T with
                      | Prop => auto
                      end
           end