Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  a : A
  l1 : list A
  IHl1 : ∀ (l2 : list A) (r : list B),
           All2 R (l1 ++ l2) r
           → ∑ r1 r2 : list B, r = r1 ++ r2 × All2 R l1 r1 × All2 R l2 r2
  l2 : list A
  r : list B
  X1 : sigma (λ _ : list A, list B)
  X : All2 R (pr1 X1) (pr2 X1)
  ============================
   ({| pr1 := a :: l1 ++ l2; pr2 := r |} = X1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      ∑ r1 r2 : list B, r = r1 ++ r2 × All2 R (a :: l1) r1 × All2 R l2 r2)


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' := X
of type
constr
id := X1
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' := X
of type
constr
id := X1
of type
constr of type tacvalue