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
  b1 : sigma (λ _ : list B, list C)
  b : All2 Q (pr1 b1) (pr2 b1)
  ============================
   ({| pr1 := y :: r; pr2 := l'' |} = b1
    → 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:
hnf in id
Level 4: evaluation returns
hnf in id;
 match type of id with
 | sigma _ =>
     let xn := fresh id "'" in
     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'
 | _ => cbv beta iota delta [TODO projection TODO projection] in id, id'
 end
where
id' := b
of type
constr
id := b1
of type
constr of type tacvalue

Level 3: evaluation returns
hnf in id;
 match type of id with
 | sigma _ =>
     let xn := fresh id "'" in
     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'
 | _ => cbv beta iota delta [TODO projection TODO projection] in id, id'
 end
where
id' := b
of type
constr
id := b1
of type
constr of type tacvalue