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)
  m : tree' A
  l : tree' A
  x : A
  r : tree' A
  Heq_m : Node111 l x r = m
  ============================
   True


DEBUG:Going to execute:
let tac H := let ph := fresh "H" in
                        destruct H as [H ph] in
           let tac2 H :=
            let ph := fresh "H" in
            let ph' := fresh "H" in
            destruct H as [H ph ph']
           in
           let tacT H := let ph := fresh "X" in
                         destruct H as [H ph] in
           let tacT2 H :=
            let ph := fresh "X" in
            let ph' := fresh "X" in
            destruct H as [H ph ph']
           in
           match goal with
           | H:exists y, _ y |- _ => tac H
           | H:{x : _ | ?P x} |- _ => tac H
           | H:{x : _ & ?P x} |- _ => tacT H
           | H:exists2 x : _, _ x & _ x |- _ => tac2 H
           | H:{x : _ | ?P x & _ x} |- _ => tac2 H
           | H:{x : _ & ?P x & _ x} |- _ => tacT2 H
           end