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


DEBUG:Going to execute:
destruct l2

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

  
  A : Type
  a : A
  l1 : list A
  x : A
  y : A
  IHl1 : ∀ l2 : list A, l1 ++ [x] = l2 ++ [y] → l1 = l2 ∧ x = y
  a0 : A
  l2 : list A
  H : a :: l1 ++ [x] = (a0 :: l2) ++ [y]
  ============================
   (a :: l1 = a0 :: l2 ∧ x = y)


DEBUG:Going to execute:
invs H
DEBUG LTAC Evaluated term: l2

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

  
  A : Type
  a : A
  l1 : list A
  x : A
  y : A
  IHl1 : ∀ l2 : list A, l1 ++ [x] = l2 ++ [y] → l1 = l2 ∧ x = y
  a0 : A
  l2 : list A
  H : a :: l1 ++ [x] = (a0 :: l2) ++ [y]
  ============================
   (a :: l1 = a0 :: l2 ∧ x = y)


DEBUG:Going to execute:
fun H => inversion H; subst; clear H