Goal:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  ============================
   (∀ (l : list A) (l0 : ∀ y : C, Q y → ∥ All (P y) l ∥) 
      (H := CoreTactics.block) (l1 : list A) (Hl : 
                                              ∀ y : C, 
                                                Q y → ∥ All (P y) l1 ∥),
      {| pr1 := l; pr2 := l0 |} = {| pr1 := l1; pr2 := Hl |}
      → map_All fn l l0 = map_All fn l1 Hl
        → let H0 := CoreTactics.block in #|map_All fn l1 Hl| = #|l1|)


DEBUG:Going to execute:
<coq-equations.plugin::refine_ho@0> $1
DEBUG LTAC Evaluated term: (fun_elim ?P ?f ?f0)

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  ============================
   (∀ Hl : ∀ y : C, Q y → ∥ All (P y) [] ∥,
      (λ (l : list A) (Hl0 : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (Hl1 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl0 |} = {| pr1 := l0; pr2 := Hl1 |}
           → x = map_All fn l0 Hl1
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl1| = #|l0|)
        [] Hl [])

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  ============================
   (∀ (x : A) (xs : list A) (h : ∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥),
      (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x0 : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
           → x0 = map_All fn l0 Hl0
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
        xs (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
      → (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x0 : list B),
           ∀ (H := CoreTactics.block) (l0 : list A) 
             (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
             {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
             → x0 = map_All fn l0 Hl0
               → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
          (x :: xs) h
          (fn x (map_All_obligation_1 x xs h)
           :: map_All fn xs (map_All_obligation_2 x xs h)))


DEBUG:Going to execute:
intros

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  Hl : ∀ y : C, Q y → ∥ All (P y) [] ∥
  ============================
   ((λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
       ∀ (H := CoreTactics.block) (l0 : list A) (Hl0 : 
                                                 ∀ y : C,
                                                 Q y → ∥ All (P y) l0 ∥),
         {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
         → x = map_All fn l0 Hl0
           → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|) []
      Hl [])

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥
  H : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
           → x = map_All fn l0 Hl0
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
        xs (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
  ============================
   ((λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
       ∀ (H := CoreTactics.block) (l0 : list A) (Hl0 : 
                                                 ∀ y : C,
                                                 Q y → ∥ All (P y) l0 ∥),
         {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
         → x = map_All fn l0 Hl0
           → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
      (x :: xs) h
      (fn x (map_All_obligation_1 x xs h)
       :: map_All fn xs (map_All_obligation_2 x xs h)))


DEBUG:Going to execute:
cbv beta

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  Hl : ∀ y : C, Q y → ∥ All (P y) [] ∥
  ============================
   (∀ (H := CoreTactics.block) (l : list A) (Hl0 : 
                                             ∀ y : C, 
                                               Q y → ∥ All (P y) l ∥),
      {| pr1 := []; pr2 := Hl |} = {| pr1 := l; pr2 := Hl0 |}
      → [] = map_All fn l Hl0
        → let H0 := CoreTactics.block in #|map_All fn l Hl0| = #|l|)

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥
  H : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
           → x = map_All fn l0 Hl0
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
        xs (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (H := CoreTactics.block) (l : list A) (Hl : 
                                             ∀ y : C, 
                                               Q y → ∥ All (P y) l ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := l; pr2 := Hl |}
      → fn x (map_All_obligation_1 x xs h)
        :: map_All fn xs (map_All_obligation_2 x xs h) = 
        map_All fn l Hl
        → let H0 := CoreTactics.block in #|map_All fn l Hl| = #|l|)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  Hl : ∀ y : C, Q y → ∥ All (P y) [] ∥
  ============================
   (∀ (H := CoreTactics.block) (l : list A) (Hl0 : 
                                             ∀ y : C, 
                                               Q y → ∥ All (P y) l ∥),
      {| pr1 := []; pr2 := Hl |} = {| pr1 := l; pr2 := Hl0 |}
      → [] = map_All fn l Hl0
        → let H0 := CoreTactics.block in #|map_All fn l Hl0| = #|l|)

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥
  H : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
           → x = map_All fn l0 Hl0
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
        xs (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (H := CoreTactics.block) (l : list A) (Hl : 
                                             ∀ y : C, 
                                               Q y → ∥ All (P y) l ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := l; pr2 := Hl |}
      → fn x (map_All_obligation_1 x xs h)
        :: map_All fn xs (map_All_obligation_2 x xs h) = 
        map_All fn l Hl
        → let H0 := CoreTactics.block in #|map_All fn l Hl| = #|l|)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim