Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → Type
  Q : B → C → Type
  R : A → C → Type
  l'' : list C
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : ∀ l'' : list C,
          All2 Q l' l''
          → (∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z) → All2 R l l''
  a1 : sigma (λ _ : list B, list C)
  a : All2 Q (pr1 a1) (pr2 a1)
  ============================
   ({| pr1 := y :: l'; pr2 := l'' |} = a1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      (∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z)
      → All2 R (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' := a
of type
ident
id := a1
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' := a
of type
ident
id := a1
of type
constr of type tacvalue