Goal:
  
  G : t
  A : Type
  B : Type
  f : A -> B -> A
  g : B -> bool
  l : list B
  acc : A
  ============================
   (fold_left f (filter g l) acc =
    fold_left (fun (acc : A) (x : B) => if g x then f acc x else acc) l acc)


DEBUG:Going to execute:
induction l in acc |- *

Goals:
    G : t  A : Type  B : Type  f : A -> B -> A  g : B -> bool  acc : A
  ============================
   (fold_left f (filter g []) acc =
    fold_left (fun (acc : A) (x : B) => if g x then f acc x else acc) [] acc)

  
  G : t
  A : Type
  B : Type
  f : A -> B -> A
  g : B -> bool
  a : B
  l : list B
  acc : A
  IHl : forall acc : A,
        fold_left f (filter g l) acc =
        fold_left (fun (acc0 : A) (x : B) => if g x then f acc0 x else acc0)
          l acc
  ============================
   (fold_left f (filter g (a :: l)) acc =
    fold_left (fun (acc : A) (x : B) => if g x then f acc x else acc)
      (a :: l) acc)


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

Goals:
    G : t  A : Type  B : Type  f : A -> B -> A  g : B -> bool  acc : A
  ============================
   (acc = acc)

  
  G : t
  A : Type
  B : Type
  f : A -> B -> A
  g : B -> bool
  a : B
  l : list B
  acc : A
  IHl : forall acc : A,
        fold_left f (filter g l) acc =
        fold_left (fun (acc0 : A) (x : B) => if g x then f acc0 x else acc0)
          l acc
  ============================
   (fold_left f (if g a then a :: filter g l else filter g l) acc =
    fold_left (fun (acc : A) (x : B) => if g x then f acc x else acc) l
      (if g a then f acc a else acc))


DEBUG:Going to execute:
auto

Goals:
    G : t  A : Type  B : Type  f : A -> B -> A  g : B -> bool  acc : A
  ============================
   (acc = acc)

  
  G : t
  A : Type
  B : Type
  f : A -> B -> A
  g : B -> bool
  a : B
  l : list B
  acc : A
  IHl : forall acc : A,
        fold_left f (filter g l) acc =
        fold_left (fun (acc0 : A) (x : B) => if g x then f acc0 x else acc0)
          l acc
  ============================
   (fold_left f (if g a then a :: filter g l else filter g l) acc =
    fold_left (fun (acc : A) (x : B) => if g x then f acc x else acc) l
      (if g a then f acc a else acc))


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