Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  i : list B
  a : A
  l : list A
  tl : list A
  tl' : list A
  IHl : ∀ i i' : list B,
          OnOne2All P i tl tl'
          → #|i'| = #|l| → OnOne2All P (i' ++ i) (l ++ tl) (l ++ tl')
  X : OnOne2All P i tl tl'
  H : #|[]| = S #|l|
  ============================
   (OnOne2All P ([] ++ i) (a :: l ++ tl) (a :: l ++ 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 ])