Goal:
  
  A : Type
  P : list A → A → Type
  Δ : list A
  d : A
  Γ : list A
  X : All_fold (λ Γ : list A, P (Γ ++ Δ)) Γ
  p : P (Γ ++ Δ) d
  IHX : All_fold P Δ → All_fold P (Γ ++ Δ)
  X0 : All_fold P Δ
  ============================
   (All_fold P (d :: Γ ++ Δ))


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 ]