Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  a0 : A
  Δ' : list A
  H : S #|Δ| = S #|Δ'|
  IHΔ : All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
        → All2_fold P Γ Γ'
          × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) Δ Δ'
  H'1 : sigma (λ _ : list A, list A)
  H' : All2_fold P (pr1 H'1) (pr2 H'1)
  ============================
   ({| pr1 := a :: Δ ++ Γ; pr2 := a0 :: Δ' ++ Γ' |} = H'1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) 
          (a :: Δ) (a0 :: Δ'))


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' := H'
of type
constr
id := H'1
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' := H'
of type
constr
id := H'1
of type
constr of type tacvalue