Goal:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (R y) (x :: xs) ∥
  X : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (R y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (P : C → A → Prop) 
           (Q' : B → Type) (args : list A) (ha : ∀ y : C,
                                                 Q y → ∥ All (R y) args ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := args; pr2 := ha |}
           → x = map_All f args ha
             → let H0 := CoreTactics.block in
               (∀ y : C, Q y → All (P y) args)
               → (∀ (x0 : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x0),
                    P y x0 → Q' (f x0 rx))
                 → ∀ y : C, Q y → All Q' (map_All f args ha)) xs
        (map_All_obligation_2 x xs h)
        (map_All f xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (H := CoreTactics.block) (P : C → A → Prop) 
      (Q' : B → Type) (args : list A) (ha : ∀ y : C, Q y → ∥ All (R y) args ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := args; pr2 := ha |}
      → f x (map_All_obligation_1 x xs h)
        :: map_All f xs (map_All_obligation_2 x xs h) = 
        map_All f args ha
        → let H0 := CoreTactics.block in
          (∀ y : C, Q y → All (P y) args)
          → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
               P y x → Q' (f x rx))
            → ∀ y : C, Q y → All Q' (map_All f args ha))


DEBUG:Going to execute:
intros _

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  Hl : ∀ y : C, Q y → ∥ All (R y) [] ∥
  ============================
   (∀ (P : C → A → Prop) (Q' : B → Type) (args : list A) 
      (ha : ∀ y : C, Q y → ∥ All (R y) args ∥),
      {| pr1 := []; pr2 := Hl |} = {| pr1 := args; pr2 := ha |}
      → [] = map_All f args ha
        → let H := CoreTactics.block in
          (∀ y : C, Q y → All (P y) args)
          → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
               P y x → Q' (f x rx))
            → ∀ y : C, Q y → All Q' (map_All f args ha))

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (R y) (x :: xs) ∥
  X : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (R y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (P : C → A → Prop) 
           (Q' : B → Type) (args : list A) (ha : ∀ y : C,
                                                 Q y → ∥ All (R y) args ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := args; pr2 := ha |}
           → x = map_All f args ha
             → let H0 := CoreTactics.block in
               (∀ y : C, Q y → All (P y) args)
               → (∀ (x0 : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x0),
                    P y x0 → Q' (f x0 rx))
                 → ∀ y : C, Q y → All Q' (map_All f args ha)) xs
        (map_All_obligation_2 x xs h)
        (map_All f xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (P : C → A → Prop) (Q' : B → Type) (args : list A) 
      (ha : ∀ y : C, Q y → ∥ All (R y) args ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := args; pr2 := ha |}
      → f x (map_All_obligation_1 x xs h)
        :: map_All f xs (map_All_obligation_2 x xs h) = 
        map_All f args ha
        → let H := CoreTactics.block in
          (∀ y : C, Q y → All (P y) args)
          → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
               P y x → Q' (f x rx))
            → ∀ y : C, Q y → All Q' (map_All f args ha))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  Hl : ∀ y : C, Q y → ∥ All (R y) [] ∥
  ============================
   (∀ (P : C → A → Prop) (Q' : B → Type) (args : list A) 
      (ha : ∀ y : C, Q y → ∥ All (R y) args ∥),
      {| pr1 := []; pr2 := Hl |} = {| pr1 := args; pr2 := ha |}
      → [] = map_All f args ha
        → let H := CoreTactics.block in
          (∀ y : C, Q y → All (P y) args)
          → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
               P y x → Q' (f x rx))
            → ∀ y : C, Q y → All Q' (map_All f args ha))

  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (R y) (x :: xs) ∥
  X : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (R y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (P : C → A → Prop) 
           (Q' : B → Type) (args : list A) (ha : ∀ y : C,
                                                 Q y → ∥ All (R y) args ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := args; pr2 := ha |}
           → x = map_All f args ha
             → let H0 := CoreTactics.block in
               (∀ y : C, Q y → All (P y) args)
               → (∀ (x0 : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x0),
                    P y x0 → Q' (f x0 rx))
                 → ∀ y : C, Q y → All Q' (map_All f args ha)) xs
        (map_All_obligation_2 x xs h)
        (map_All f xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (P : C → A → Prop) (Q' : B → Type) (args : list A) 
      (ha : ∀ y : C, Q y → ∥ All (R y) args ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := args; pr2 := ha |}
      → f x (map_All_obligation_1 x xs h)
        :: map_All f xs (map_All_obligation_2 x xs h) = 
        map_All f args ha
        → let H := CoreTactics.block in
          (∀ y : C, Q y → All (P y) args)
          → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
               P y x → Q' (f x rx))
            → ∀ y : C, Q y → All Q' (map_All f args ha))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim