Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : 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 := Γ; pr2 := a :: 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 Γ in
           let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d a))


DEBUG:Going to execute:
match type of id with
           | sigma _ =>
               let xn := fresh id "'" in
               destruct id as [xn id]; DepElim.decompose_exists xn id;
                cbv beta iota delta [TODO projection TODO projection]
                 in id, id'; DepElim.decompose_exists id id'
           | _ =>
               cbv beta iota delta [TODO projection TODO projection]
                in id, id'
           end