Goal:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  h : OnOne2i P (S i) tl tl'
  i' : nat
  x : A
  y : A
  u : list A
  v : list A
  a : P i' x y
  H : tl = u ++ x :: v
  H0 : tl' = u ++ y :: v
  ============================
   (hd :: tl = (hd :: u) ++ x :: v)


DEBUG:Going to execute:
match goal with
           | |- _ → _ => intro; t_tauto_intuit
           | |- _ => t_reduce; t_solver
           end