Goal:
  
  T : Type -> Type
  M : Monad T
  A : Type
  P : nat -> A -> Type
  Q : A -> Type
  f : forall (n : nat) (x : A), ∥ Q x ∥ -> T (∥ P n x ∥)
  n : nat
  a : A
  ============================
   (forall l : list A,
    ∥ All Q (a :: l) ∥ ->
    ∥ P n a ∥ -> ∥ Alli P (S n) l ∥ -> ∥ Alli P n (a :: l) ∥)


DEBUG:Going to execute:
<coq-equations.plugin::simplify@0> $1