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 l : tree' A) (x : A) (r : tree' A),
    Node111 l x r = m -> not_trivially_empty (Nodes l) (Some x) (Nodes r))


DEBUG:Going to execute:
simpl in *; program_simplify