Goal:
  
  A : Type
  a : A
  x : A
  l : list A
  IHl : l ≠ [] → l = remove_last l ++ [last l a]
  H : l ++ [x] ≠ []
  ============================
   (l ++ [x] = l ++ [x])


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 ])