Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (H := CoreTactics.block) (f0 : A → B) (l : list A) 
      (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := x :: xs; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → f x (map_InP_obligations_obligation_1 x xs)
          :: map_InP xs
               (λ (x0 : A) (inx : In x0 xs),
                  f x0 (map_InP_obligations_obligation_2 x xs x0 inx)) =
          map_InP l g → let H0 := CoreTactics.block in map_InP l g = map f0 l)


DEBUG:Going to execute:
intros _

Goals:
    A : Type  B : Type  f : ∀ x : A, In x [] → B
  ============================
   (∀ (f0 : A → B) (l : list A) (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := []; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → [] = map_InP l g
          → let H := CoreTactics.block in map_InP l g = map f0 l)

  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (f0 : A → B) (l : list A) (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := x :: xs; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → f x (map_InP_obligations_obligation_1 x xs)
          :: map_InP xs
               (λ (x0 : A) (inx : In x0 xs),
                  f x0 (map_InP_obligations_obligation_2 x xs x0 inx)) =
          map_InP l g → let H := CoreTactics.block in map_InP l g = map f0 l)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  B : Type  f : ∀ x : A, In x [] → B
  ============================
   (∀ (f0 : A → B) (l : list A) (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := []; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → [] = map_InP l g
          → let H := CoreTactics.block in map_InP l g = map f0 l)

  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           f x0 (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              f x0 (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (∀ (f0 : A → B) (l : list A) (g : ∀ x : A, In x l → B),
      g = (λ (x : A) (_ : In x l), f0 x)
      → {| pr1 := x :: xs; pr2 := f |} = {| pr1 := l; pr2 := g |}
        → f x (map_InP_obligations_obligation_1 x xs)
          :: map_InP xs
               (λ (x0 : A) (inx : In x0 xs),
                  f x0 (map_InP_obligations_obligation_2 x xs x0 inx)) =
          map_InP l g → let H := CoreTactics.block in map_InP l g = map f0 l)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim