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)
  ============================
   (forall m r : tree' A,
    Node001 r = m -> not_trivially_empty Empty None (Nodes r))


DEBUG:Going to execute:
simpl in *; program_simplify