Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  a0 : A
  ls2 : list A
  n : nat
  X2 : Alli (P a0) (S n) ls1
  X3 : All (λ x : A, Alli (P x) (S n) ls1) ls2
  X1 : P a0 n a
  X4 : All (λ x : A, P x n a) ls2
  X0 : All (λ x : A, P x n a) (a0 :: ls2)
  X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) 
         (S n) ls1
  ============================
   (All (λ x : A, Alli (P x) n (a :: ls1)) ls2)


DEBUG:Going to execute:
match reverse goal with
           | id:(?X1 → ?X2) → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (X1 → X2);
                     [ exact
                     id
                     | generalize (λ y : X2, id (λ x : X1, y)); intro; clear
                        id; (solve [ t_tauto_intuit ]) ] ]
           | id:¬ ?X1 → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (¬ X1);
                     [ exact
                     id
                     | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
           | |- ?X1 =>
                 <Coq.Init.Tauto.is_disj> flags X1; (solve
                  [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
           end