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 : #|Γ| = #|Γ'|
  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' : All2_fold P (a :: Δ ++ Γ) (a0 :: Δ' ++ Γ')
  H'0 := {|
           pr1 := {| pr1 := a :: Δ ++ Γ; pr2 := a0 :: Δ' ++ Γ' |}; pr2 := H'
         |}
      : sigma
          (λ index : sigma (λ _ : list A, list A),
             All2_fold P (pr1 index) (pr2 index))
  H'1 := {| pr1 := a :: Δ ++ Γ; pr2 := a0 :: Δ' ++ Γ' |}
      : sigma (λ _ : list A, list A)
  H'2 : (λ index : sigma (λ _ : list A, list A),
           All2_fold P (pr1 index) (pr2 index)) H'1
  ============================
   (H' = H'2
    → 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:
clear id' id