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
  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
  b : All2 Q (y :: r) l''
  b0 := {| pr1 := {| pr1 := y :: r; pr2 := l'' |}; pr2 := b |}
     : sigma
         (λ index : sigma (λ _ : list B, list C),
            All2 Q (pr1 index) (pr2 index))
  ============================
   (let H := CoreTactics.block in
    All2i R n (x :: l) l''
    → (∀ (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) l'')


DEBUG:Going to execute:
let id'1 := fresh id' in
           let id'2 := fresh id' in
           set (id'2 := pr2 id'); set (id'1 := pr1 id') in id'2;
            hnf in (value of id'1), (value of id'2);
            try red in (type of id'2);
            match goal with
            | id'1:=?t:_
              |- _ =>
                  generalize (eq_refl : t = id'1); clearbody id'2 id'1; clear
                   id' id; try unfold signature in id'2; 
                   hnf in id'2; simpl in id'2; rename id'2 into id;
                   cont id id id'1 t
            end