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
  c1 : sigma (λ _ : nat, sigma (λ _ : list A, list C))
  c : All2i R (pr1 c1) (pr1 (pr2 c1)) (pr2 (pr2 c1))
  ============================
   ({| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |} = c1
    → 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:
destruct id as [xn id]; DepElim.decompose_exists xn id;
            cbv beta iota delta [TODO projection TODO projection] in id, id';
            DepElim.decompose_exists id id'