Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  H : All2_fold Q (d :: Γ) Γ'
  H0 := {| pr1 := {| pr1 := d :: Γ; pr2 := Γ' |}; pr2 := H |}
     : sigma
         (λ index : sigma (λ _ : list A, list A),
            All2_fold Q (pr1 index) (pr2 index))
  H1 := {| pr1 := d :: Γ; pr2 := Γ' |} : sigma (λ _ : list A, list A)
  H2 := H
     : (λ index : sigma (λ _ : list A, list A),
          All2_fold Q (pr1 index) (pr2 index)) H1
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') (d :: Γ) Γ')


DEBUG:Going to execute:
generalize (eq_refl : t = id'1); clearbody id'2 id'1; clear id' id;
            try unfold signature in id'2; hnf in id'2; 
            simpl in id'2; rename id'2 into id