Goal:
  
  A : Type
  a : A
  l1 : list A
  x : A
  y : A
  IHl1 : ∀ l2 : list A, (a :: l1) ++ [x] = l2 ++ [y] → a :: l1 = l2 ∧ x = y
  H2 : (a :: l1) ++ [x] = []
  ============================
   (y :: a :: l1 = (a :: l1) ++ [x] ∧ x = y)


DEBUG:Going to execute:
inversion H; subst