Goal:
  
  A : Type
  B : Type
  C : Type
  P : nat → A → B → Type
  Q : B → C → Type
  R : nat → A → C → Type
  S : nat → A → C → Type
  y0 : C
  l' : list C
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : P n x y
  a : All2i P (Datatypes.S n) l r
  q : Q y y0
  b : All2 Q r l'
  c1' : nat
  x0 : A
  y1 : C
  l0 : list A
  r1 : list C
  r2 : R c1' x0 y1
  c : All2i R (Datatypes.S c1') l0 r1
  ============================
   ({| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y0 :: l' |} |} =
    {| pr1 := c1'; pr2 := {| pr1 := x0 :: l0; pr2 := y1 :: r1 |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (x : A) (y : B) (z : C),
         P n x y → Q y z → R n x z → S n x z)
      → (∀ l'' : list C,
           All2 Q r l''
           → All2i R (Datatypes.S n) l l'' → All2i S (Datatypes.S n) l l'')
        → let H0 := CoreTactics.block in All2i S n (x :: l) (y0 :: l'))


DEBUG:Going to execute:
match goal with
           | |- context [ rew <- [_] eq_refl in _ ] =>
                 progress simpl eq_rect_r
           | |- context [ rew [_] eq_refl in _ ] => progress simpl eq_rect
           | |- context [ Prop.Logic.transport _ eq_refl _ ] =>
                 progress simpl Prop.Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ → ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- ∀ x, _ => let H := fresh x in
                          intro
                          H
           | |- _ => intro
           end