Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    let H1 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


DEBUG:Going to execute:
intros _

Goals:
    A : Type  B : Type  R : nat → A → B → Type  n : nat
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x : A) (y : B),
         (if i <? n then False else nth_error [] (i - n) = Some x) × R i x y)
      n [] [])

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  B : Type  R : nat → A → B → Type  n : nat
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x : A) (y : B),
         (if i <? n then False else nth_error [] (i - n) = Some x) × R i x y)
      n [] [])

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


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

Goals:
    A : Type  B : Type  R : nat → A → B → Type  n : nat
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x : A) (y : B),
         (if i <? n then False else nth_error [] (i - n) = Some x) × R i x y)
      n [] [])

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


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

Goals:
    A : Type  B : Type  R : nat → A → B → Type  n : nat
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x : A) (y : B),
         (if i <? n then False else nth_error [] (i - n) = Some x) × R i x y)
      n [] [])

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  B : Type  R : nat → A → B → Type  n : nat
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x : A) (y : B),
         (if i <? n then False else nth_error [] (i - n) = Some x) × R i x y)
      n [] [])

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2i
      (λ (i : nat) (x0 : A) (y : B),
         (if i <? n then False else nth_error (x :: l) (i - n) = Some x0)
         × R i x0 y) n (x :: l) (y :: r))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim