Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  HP : ∀ (Γ Γ' Γ'' : list A) (x y z : A),
         All2_fold P Γ Γ'
         → All2_fold P Γ' Γ''
           → All2_fold P Γ Γ'' → P Γ Γ' x y → P Γ' Γ'' y z → P Γ Γ'' x z
  z : list A
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ z : list A, All2_fold P Γ' z → All2_fold P Γ z
  H'1' : list A
  H'1 : list A
  H' : All2_fold P (pr1 {| pr1 := H'1'; pr2 := H'1 |})
         (pr2 {| pr1 := H'1'; pr2 := H'1 |})
  ============================
   ({| pr1 := d' :: Γ'; pr2 := z |} = {| pr1 := H'1'; pr2 := H'1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2_fold P (d :: Γ) z)


DEBUG:Going to execute:
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