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
  n : nat
  c : All2i R n [] []
  c0 := {|
          pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := c
        |}
     : sigma
         (λ index : sigma (λ _ : nat, sigma (λ _ : list A, list C)),
            All2i R (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  ============================
   (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)
    → let H0 := CoreTactics.block in All2i S n [] [])


DEBUG:Going to execute:
hnf in (type of id')