Goal:
    A : Type  B : Type  f : A → A → B  _a_ : A  _l_ : list A
  ============================
   (f _a_ _a_ :: map (λ x : A, f x x) _l_ =
    f _a_ _a_ :: map (λ x : A, f x x) _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 ])