Goal:
  
  T : Type -> Type
  M : Monad T
  A : Type
  P : nat -> A -> Type
  l0 : list A
  k : nat
  f : forall (n : nat) (x : A),
      nth_error l0 n = Some x -> T (∥ P (k + n) x ∥)
  a : A
  l : list A
  Heq_l : a :: l = l0
  ============================
   (match l0 with
    | [] => None
    | x :: _ => Some x
    end = Some a)


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