Goal:
  
  A : Type
  B : Type
  f : nat → A
  a : B
  l : list B
  IHl : ∀ (f : nat → A) (l' : list B),
          #|l| = #|l'|
          → mapi (λ (i : nat) (_ : B), f i) l =
            mapi (λ (i : nat) (_ : B), f i) l'
  ============================
   (#|a :: l| = #|[]|
    → mapi (λ (i : nat) (_ : B), f i) (a :: l) =
      mapi (λ (i : nat) (_ : B), f i) [])


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 ])