Goal:
  
  A : Type
  size : A → nat
  l : list A
  f : A → A
  H : ∀ x : A, size x = size (f x)
  ============================
   (list_size size (map f l) = list_size size l)


DEBUG:Going to execute:
induction l

Goals:
    A : Type  size : A → nat  f : A → A  H : ∀ x : A, size x = size (f x)
  ============================
   (list_size size (map f []) = list_size size [])

  
  A : Type
  size : A → nat
  a : A
  l : list A
  f : A → A
  H : ∀ x : A, size x = size (f x)
  IHl : list_size size (map f l) = list_size size l
  ============================
   (list_size size (map f (a :: l)) = list_size size (a :: l))


DEBUG:Going to execute:
simpl
DEBUG LTAC Evaluated term: l

Goals:
    A : Type  size : A → nat  f : A → A  H : ∀ x : A, size x = size (f x)
  ============================
   (0 = 0)

  
  A : Type
  size : A → nat
  a : A
  l : list A
  f : A → A
  H : ∀ x : A, size x = size (f x)
  IHl : list_size size (map f l) = list_size size l
  ============================
   (S (size (f a) + list_size size (map f l)) = S (size a + list_size size l))


DEBUG:Going to execute:
auto

Goals:
    A : Type  size : A → nat  f : A → A  H : ∀ x : A, size x = size (f x)
  ============================
   (0 = 0)

  
  A : Type
  size : A → nat
  a : A
  l : list A
  f : A → A
  H : ∀ x : A, size x = size (f x)
  IHl : list_size size (map f l) = list_size size l
  ============================
   (S (size (f a) + list_size size (map f l)) = S (size a + list_size size l))


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3