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


DEBUG:Going to execute:
solve
[ do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]
| case not_locked_false_eq_true; Ltac.assumption
| match goal with
  | H:¬ _ |- _ => solve [ case H; trivial ]
  end ]