Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e : #|bs| = #|tl|
  b : B
  bs0 : list B
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P b hd0 hd'0
  e0 : #|bs0| = #|tl0|
  H0 := {|
          pr1 := b;
          pr2 :=
            {|
              pr1 := bs0;
              pr2 :=
                {|
                  pr1 := hd0;
                  pr2 :=
                    {|
                      pr1 := hd'0;
                      pr2 :=
                        {| pr1 := tl0; pr2 := {| pr1 := p0; pr2 := e0 |} |}
                    |}
                |}
            |}
        |}
     : sigma
         (λ b : B,
            sigma
              (λ bs : list B,
                 sigma
                   (λ hd : A,
                      sigma
                        (λ hd' : A,
                           sigma
                             (λ tl : list A,
                                sigma (λ _ : P b hd hd', #|bs| = #|tl|))))))
  H : {|
        pr1 := b0;
        pr2 :=
          {|
            pr1 := bs;
            pr2 :=
              {|
                pr1 := hd;
                pr2 :=
                  {|
                    pr1 := hd';
                    pr2 := {| pr1 := tl; pr2 := {| pr1 := p; pr2 := e |} |}
                  |}
              |}
          |}
      |} = H0
  ============================
   ({|
      pr1 :=
        {| pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
      pr2 := OnOne2All_hd P b0 bs hd hd' tl p e
    |} =
    {|
      pr1 :=
        {|
          pr1 := b :: bs0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
        |};
      pr2 := OnOne2All_hd P b bs0 hd0 hd'0 tl0 p0 e0
    |})


DEBUG:Going to execute:
pattern sigma rhs
DEBUG LTAC Evaluated term: {|
                             pr1 := b;
                             pr2 :=
                               {|
                                 pr1 := bs0;
                                 pr2 :=
                                   {|
                                     pr1 := hd0;
                                     pr2 :=
                                       {|
                                         pr1 := hd'0;
                                         pr2 :=
                                           {|
                                             pr1 := tl0;
                                             pr2 :=
                                               {| pr1 := p0; pr2 := e0 |}
                                           |}
                                       |}
                                   |}
                               |}
                           |}