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' : All2_fold P (d' :: Γ') z
  H'0 := {| pr1 := {| pr1 := d' :: Γ'; pr2 := z |}; pr2 := H' |}
      : sigma
          (λ index : sigma (λ _ : list A, list A),
             All2_fold P (pr1 index) (pr2 index))
  H'1 : 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
  ============================
   ({| pr1 := d' :: Γ'; pr2 := z |} = H'1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2_fold P (d :: Γ) z)


DEBUG:Going to execute:
<coq-core.plugins.ltac::clear@0> $1