Goal:
  
  A : Type
  B : Type
  a0 : A
  l : list A
  a : B
  l' : list B
  default : A
  IHl' : ∀ l : list A,
           #|l| = #|l'| → mapi (λ (i : nat) (_ : B), nth i l default) l' = l
  ============================
   (S #|l| = S #|l'|
    → mapi
        (λ (i : nat) (_ : B),
           match i with
           | 0 => a0
           | S m => nth m l default
           end) (a :: l') = a0 :: l)


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 ])