Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  b : B
  bs0 : list B
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b1 : OnOne2All P bs0 tl0 tl'0
  H0 := {|
          pr1 := b;
          pr2 :=
            {|
              pr1 := bs0;
              pr2 :=
                {|
                  pr1 := hd0;
                  pr2 :=
                    {| pr1 := tl0; pr2 := {| pr1 := tl'0; pr2 := b1 |} |}
                |}
            |}
        |}
     : sigma
         (λ _ : B,
            sigma
              (λ bs : list B,
                 sigma
                   (λ _ : A,
                      sigma
                        (λ tl : list A,
                           sigma (λ tl' : list A, OnOne2All P bs tl tl')))))
  H : {|
        pr1 := b0;
        pr2 :=
          {|
            pr1 := bs;
            pr2 :=
              {|
                pr1 := hd;
                pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
              |}
          |}
      |} = H0
  ============================
   ({|
      pr1 :=
        {| pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
      pr2 := OnOne2All_tl P b0 bs hd tl tl' a
    |} =
    {|
      pr1 :=
        {|
          pr1 := pr1 H0 :: pr1 (pr2 H0);
          pr2 :=
            {|
              pr1 := pr1 (pr2 (pr2 H0)) :: pr1 (pr2 (pr2 (pr2 H0)));
              pr2 := pr1 (pr2 (pr2 H0)) :: pr1 (pr2 (pr2 (pr2 (pr2 H0))))
            |}
        |};
      pr2 :=
        OnOne2All_tl P (pr1 H0) (pr1 (pr2 H0)) (pr1 (pr2 (pr2 H0)))
          (pr1 (pr2 (pr2 (pr2 H0)))) (pr1 (pr2 (pr2 (pr2 (pr2 H0)))))
          (pr2 (pr2 (pr2 (pr2 (pr2 H0)))))
    |})


DEBUG:Going to execute:
clearbody rhs