Goal:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  z1'0 : list A
  z1 : list B
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) z1' z1'0 z1
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := z1'0; pr2 := z1 |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  x0 : A
  y0 : B
  l : list A
  r : list B
  r0 : R z1' x0 (g x0 y0)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) (S z1') l r
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := x0 :: l; pr2 := y0 :: r |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  x0 : A
  y0 : B
  l : list A
  r : list B
  r0 : R z1' x0 (g x0 y0)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) (S z1') l r
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := x0 :: l; pr2 := y0 :: r |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  x0 : A
  y0 : B
  l : list A
  r : list B
  r0 : R z1' x0 (g x0 y0)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) (S z1') l r
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := x0 :: l; pr2 := y0 :: r |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  x0 : A
  y0 : B
  l : list A
  r : list B
  r0 : R z1' x0 (g x0 y0)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) (S z1') l r
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := x0 :: l; pr2 := y0 :: r |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z1' : nat
  x0 : A
  y0 : B
  l : list A
  r : list B
  r0 : R z1' x0 (g x0 y0)
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) (S z1') l r
  ============================
   ({| pr1 := k; pr2 := {| pr1 := x :: xs; pr2 := y :: ys |} |} =
    {| pr1 := z1'; pr2 := {| pr1 := x0 :: l; pr2 := y0 :: r |} |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in R k x (g x y))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim