Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  i : list B
  b : B
  i' : list B
  tl : list A
  tl' : list A
  ============================
   (OnOne2All P i tl tl'
    → #|b :: i'| = 0 → OnOne2All P ((b :: i') ++ i) tl tl')


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 ])