Goal:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  H0 := {|
          pr1 := i0;
          pr2 :=
            {|
              pr1 := hd0;
              pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
            |}
        |}
     : sigma
         (λ i : nat,
            sigma
              (λ hd : A, sigma (λ hd' : A, sigma (λ _ : list A, P i hd hd'))))
  H : {|
        pr1 := i;
        pr2 :=
          {|
            pr1 := hd;
            pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
          |}
      |} = H0
  ============================
   ({|
      pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
      pr2 := OnOne2i_hd P i hd hd' tl p
    |} =
    {|
      pr1 :=
        {|
          pr1 := pr1 H0;
          pr2 :=
            {|
              pr1 := pr1 (pr2 H0) :: pr1 (pr2 (pr2 (pr2 H0)));
              pr2 := pr1 (pr2 (pr2 H0)) :: pr1 (pr2 (pr2 (pr2 H0)))
            |}
        |};
      pr2 :=
        OnOne2i_hd P (pr1 H0) (pr1 (pr2 H0)) (pr1 (pr2 (pr2 H0)))
          (pr1 (pr2 (pr2 (pr2 H0)))) (pr2 (pr2 (pr2 (pr2 H0))))
    |})


DEBUG:Going to execute:
clearbody rhs