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