Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  a : A
  Γ : list A
  Γ' : list A
  Hrel1' : list A
  Hrel1 : list A
  Hrel : All2_fold P (pr1 {| pr1 := Hrel1'; pr2 := Hrel1 |})
           (pr2 {| pr1 := Hrel1'; pr2 := Hrel1 |})
  ============================
   ({| pr1 := a :: Γ; pr2 := Γ' |} = {| pr1 := Hrel1'; pr2 := Hrel1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      ∑ d' : A,
        nth_error Γ' 0 = Some d'
        × (let Γs := skipn 1 (a :: Γ) in
           let Γs' := skipn 1 Γ' in All2_fold P Γs Γs' × P Γs Γs' a d'))


DEBUG:Going to execute:
DepElim.decompose_exists xn id