Goal:
  
  A : Type
  P : nat → A → Type
  n : nat
  x : A
  Γ : list A
  IHΓ : All_fold (λ (Γ : list A) (d : A), P (n + #|Γ|) d) (List.rev Γ)
        → Alli P n Γ
  a : All_fold (λ (Γ : list A) (d : A), P (n + #|Γ|) d) (List.rev Γ)
  p : P (n + #|List.rev Γ|) x
  ============================
   (Alli P (n + #|Γ|) [x])


DEBUG:Going to execute:
trivial; hnf; intros; (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 ])