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


DEBUG:Going to execute:
induction l

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

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


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

Goals:
  
  A : Type
  sizeA : A → nat
  B : Type
  sizeB : B → nat
  f : A → B
  H : ∀ x : A, sizeA x = sizeB (f x)
  ============================
   (0 = 0)

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


DEBUG:Going to execute:
auto

Goals:
  
  A : Type
  sizeA : A → nat
  B : Type
  sizeB : B → nat
  f : A → B
  H : ∀ x : A, sizeA x = sizeB (f x)
  ============================
   (0 = 0)

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


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