Goal:
  
  A : Type
  B : Type
  a : B
  l' : list B
  default : A
  IHl' : ∀ l : list A,
           #|l| = #|l'| → mapi (λ (i : nat) (_ : B), nth i l default) l' = l
  H : 0 = S #|l'|
  ============================
   (mapi (λ (i : nat) (_ : B), match i with
                               | 0 | _ => default
                               end) (a :: l') = [])


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 ]