Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  H1 : sigma (λ _ : list A, list A)
  H : All2_fold Q (pr1 H1) (pr2 H1)
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = 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') Γ
        (d :: Γ0))


DEBUG:Going to execute:
destruct id as [xn id]; DepElim.decompose_exists xn id;
            cbv beta iota delta [TODO projection TODO projection] in id, id'