reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve p for Prime;
reserve a,b,c,d for Element of GF(p);
reserve K for Ring;
reserve a1,a2,a3,a4,a5,a6 for Element of K;
reserve px,py,pz for object;
reserve Px,Py,Pz for Element of GF(p);
reserve P for Element of ProjCo(GF(p));
reserve O for Element of EC_SetProjCo(a,b,p);

theorem Th63:
  for p be 5_or_greater Prime, z be Element of EC_WParam p,
  g2, g3, g4, g8, gf1, gf2, gf3, gf4 be Element of GF(p),
  P be Element of EC_SetProjCo(z`1,z`2,p),
  R be Element of
  [:the carrier of GF(p), the carrier of GF(p), the carrier of GF(p):]
  st g2 = 2 mod p & g3 = 3 mod p & g4 = 4 mod p & g8 = 8 mod p &
  gf1 = z`1*(P`3_3 |^2) + g3*(P`1_3 |^2) & gf2 = P`2_3*(P`3_3) &
  gf3 = P`1_3*(P`2_3)*gf2 & gf4 = (gf1 |^2) - g8*gf3 &
  R = [g2*gf4*gf2, gf1*(g4*gf3-gf4) - g8*(P`2_3 |^2)*(gf2 |^2), g8*(gf2 |^3)]
  holds g4*(gf2 |^2)*(P`3_3 |^2)*
  ((R`2_3 |^2)*(R`3_3) - ((R`1_3 |^3) +
    z`1*(R`1_3)*(R`3_3 |^2) + z`2*(R`3_3 |^3))) = 0.GF(p)
  proof
    let p be 5_or_greater Prime, z be Element of EC_WParam p,
    g2, g3, g4, g8, gf1, gf2, gf3, gf4 be Element of GF(p),
    P be Element of EC_SetProjCo(z`1,z`2,p),
    R be Element of
    [:the carrier of GF(p), the carrier of GF(p), the carrier of GF(p):]
    such that
    A1: g2 = 2 mod p & g3 = 3 mod p & g4 = 4 mod p & g8 = 8 mod p and
    A2:  gf1 = z`1*(P`3_3 |^2) + g3*(P`1_3 |^2) & gf2 = P`2_3*(P`3_3) &
    gf3 = P`1_3*(P`2_3)*gf2 & gf4 = (gf1 |^2) - g8*gf3 and
    A3: R = [g2*gf4*gf2, gf1*(g4*gf3-gf4) - g8*(P`2_3 |^2)*(gf2 |^2),
    g8*(gf2 |^3)];
    set a = z`1;
    set b = z`2;
    A4: g4 = (2*2) mod p by A1
    .= g2*g2 by A1,EC_PF_1:18;
    then A5: g4 = g2 |^2 by EC_PF_1:22;
    A6: g8 = (2*4) mod p by A1
    .= g2*g4 by A1,EC_PF_1:18;
    A7: g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))
    = (g2 |^2)*(gf2 |^2)*(P`3_3 |^2)*(R`2_3 |^2)*(R`3_3) by A5,GROUP_1:def 3
    .= ((g2*gf2) |^2)*(P`3_3 |^2)*(R`2_3 |^2)*(R`3_3) by BINOM:9
    .= (((g2*gf2)*(P`3_3)*(R`2_3)) |^2)*(R`3_3) by Th13
    .= ((-(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))
              +g2*gf2*(P`2_3)*(R`3_3))) |^2)*(R`3_3)
    by A1,A2,A3,Th59
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))+g2*gf2*(P`2_3)*(R`3_3)) |^2)*(R`3_3)
           by Th1
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
           +g2*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(g2*gf2*(P`2_3)*(R`3_3))+((g2*gf2*(P`2_3)*(R`3_3)) |^2))*(R`3_3)
            by A1,Th25
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
      +g2*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(g2*(gf2*(P`2_3)*(R`3_3)))+((g2*gf2*(P`2_3)*(R`3_3)) |^2))*(R`3_3)
          by Th11
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
    +g2*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *g2*(gf2*(P`2_3)*(R`3_3))+((g2*gf2*(P`2_3)*(R`3_3)) |^2))*(R`3_3)
               by GROUP_1:def 3
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
  +g2*g2*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(gf2*(P`2_3)*(R`3_3))+((g2*gf2*(P`2_3)*(R`3_3)) |^2))*(R`3_3)
           by GROUP_1:def 3
    .=  (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
         +g4*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(gf2*(P`2_3)*(R`3_3))+((g2*gf2*(P`2_3*(R`3_3))) |^2))*(R`3_3)
            by A4,GROUP_1:def 3
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
   +g4*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(gf2*(P`2_3)*(R`3_3))+(g2 |^2)*(gf2 |^2)*((P`2_3*(R`3_3)) |^2))*(R`3_3)
          by Th13
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
     +g4*(gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(gf2*(P`2_3)*(R`3_3))+g4*(gf2 |^2)*((P`2_3 |^2)*(R`3_3 |^2)))*(R`3_3)
    by A5,BINOM:9
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
          +g4*gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))
    *(gf2*(P`2_3)*(R`3_3))+g4*(gf2 |^2)*((P`2_3 |^2)*(R`3_3 |^2)))*(R`3_3)
            by GROUP_1:def 3
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
          +g4*gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))
    *(gf2*(P`2_3)*(R`3_3))+g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^2))*(R`3_3)
          by GROUP_1:def 3
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
          +g4*gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))
    *gf2*(P`2_3)*(R`3_3)
           +g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^2))*(R`3_3) by Th11
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
          +g4*gf1*((P`3_3*(R`1_3)-P`1_3*(R`3_3))
    *gf2*(P`2_3))*(R`3_3)
     +g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^2))*(R`3_3) by Th11
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
          +g4*gf1*(gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3)+g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^2))*(R`3_3) by GROUP_1:def 3
    .= (((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)
    +g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3))
    *(R`3_3)+g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^2))*(R`3_3) by Th11
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
    +((g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3))*(R`3_3)+((g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^2))*(R`3_3)
          by Th14
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
     +(g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3*(R`3_3))+(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^2)*(R`3_3)
    by GROUP_1:def 3
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3*(R`3_3))+(g4*(gf2 |^2)*(P`2_3 |^2))*((R`3_3 |^2)*(R`3_3))
      by GROUP_1:def 3
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3*(R`3_3))+(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^(2+1)) by EC_PF_1:24
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)-P`1_3*(R`3_3)))
    *(R`3_3 |^2)+(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3) by EC_PF_1:22
    .= ((gf1*(P`3_3*(R`1_3)-P`1_3*(R`3_3))) |^2)*(R`3_3)
           +g4*gf1*gf2*(P`2_3)*(R`3_3 |^2)
    *(P`3_3*(R`1_3)-P`1_3*(R`3_3))+g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^3)
  by GROUP_1:def 3
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2))*(R`3_3)
        +g4*gf1*gf2*(P`2_3)*(R`3_3 |^2)
    *(P`3_3*(R`1_3)-P`1_3*(R`3_3))+g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^3)
        by BINOM:9
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +((g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))
    *(P`3_3*(R`1_3))-(g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))*(P`1_3*(R`3_3)))
   +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by VECTSP_1:11
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))
    *(P`3_3*(R`1_3))-(g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))*(P`1_3*(R`3_3))
    +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by ALGSTR_1:7
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
          +g4*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3))
    *(R`3_3 |^2)-(g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))*(P`1_3*(R`3_3))
          +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
        +g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)
    *(R`3_3 |^2)-(g4*gf1*gf2*(P`2_3)*(R`3_3 |^2))*(P`1_3*(R`3_3))
    +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))
    *(R`3_3 |^2)-g4*gf1*gf2*(P`2_3)*(R`3_3 |^2)*(P`1_3)*(R`3_3)
   +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))
    *(R`3_3 |^2)-g4*gf1*gf2*(P`2_3)*(P`1_3)*(R`3_3 |^2)*(R`3_3)
    +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))
    *(R`3_3 |^2)-g4*gf1*gf2*(P`2_3)*(P`1_3)*((R`3_3 |^2)*(R`3_3))
    +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
            +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))
    *(R`3_3 |^2)-g4*gf1*gf2*(P`2_3)*(P`1_3)*(R`3_3 |^(2+1))
      +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by EC_PF_1:24
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
   +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))
    *(R`3_3 |^2)-(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
          +g4*(gf2 |^2)*(P`2_3 |^2)
    *(R`3_3 |^3) by GROUP_1:def 3;
    A8: -g4*(gf2 |^2)*(P`3_3 |^2)*(a*(R`1_3)*(R`3_3 |^2))
    = -(g2*g2)*(gf2 |^2)*(P`3_3 |^2)*(R`1_3)*a*(R`3_3 |^2) by A4,Th11
    .= -(g2*(g2*(gf2 |^2)*(P`3_3 |^2)))*(R`1_3)*a*(R`3_3 |^2) by Th11
    .= -g2*(R`1_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*a*(R`3_3 |^2) by GROUP_1:def 3
    .= -g2*(R`1_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*a*(R`3_3*(R`3_3)) by EC_PF_1:22
    .= -g2*(R`1_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*a*(R`3_3)*(R`3_3)
         by GROUP_1:def 3
    .= -g2*(R`1_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*(R`3_3)*a*(R`3_3)
            by GROUP_1:def 3
    .= -g2*(R`1_3)*(R`3_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*a*(R`3_3)
           by GROUP_1:def 3
    .= -g2*(R`1_3)*(R`3_3)*(g2*(gf2 |^2)*(P`3_3 |^2))*(a*(R`3_3))
          by GROUP_1:def 3
     .= -g2*(R`1_3)*(R`3_3)*((g2*(gf2 |^2)*(P`3_3 |^2))*(a*(R`3_3)))
            by GROUP_1:def 3
    .= -g2*(R`1_3)*(R`3_3)*(gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    +(gf2 |^2)*(g4*(P`1_3)*(P`3_3)*(R`1_3)+g2*(P`1_3 |^2)*(R`3_3)))
            by A1,A2,A3,Th62
    .= -((g2*(R`1_3)*(R`3_3))*(gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)
             -gf1*(P`1_3)))
    +(g2*(R`1_3)*(R`3_3))*((gf2 |^2)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
    +g2*(P`1_3 |^2)*(R`3_3))))
    by VECTSP_1:def 7
    .= -(g2*(R`1_3)*(R`3_3))*((gf2 |^2)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
     +g2*(P`1_3 |^2)*(R`3_3)))
    -(g2*(R`1_3)*(R`3_3))*(gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3)))
               by VECTSP_1:17
    .= -(g2*(R`1_3)*(R`3_3))*(gf2 |^2)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
           +g2*(P`1_3 |^2)*(R`3_3))
    -(g2*(R`1_3)*(R`3_3))*(gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3)))
           by GROUP_1:def 3
    .= -(g2*(R`1_3)*(R`3_3))*(gf2 |^2)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
           +g2*(P`1_3 |^2)*(R`3_3))
    -(g2*(R`1_3)*(R`3_3))*(gf1*(P`3_3)*(R`3_3))*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(R`1_3)*(gf2 |^2)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
             +g2*(P`1_3 |^2)*(R`3_3))
    -g2*(R`1_3)*(R`3_3)*(gf1*(P`3_3)*(R`3_3))*(g2*gf2*(P`2_3)-gf1*(P`1_3))
          by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
              +g2*(P`1_3 |^2)*(R`3_3))
    -g2*(R`1_3)*(R`3_3)*(gf1*(P`3_3)*(R`3_3))*(g2*gf2*(P`2_3)-gf1*(P`1_3))
           by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
             +g2*(P`1_3 |^2)*(R`3_3))
    -g2*(R`1_3)*(R`3_3)*gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
          by Th11
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
            +g2*(P`1_3 |^2)*(R`3_3))
    -g2*(R`1_3*(R`3_3))*gf1*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
          by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
          +g2*(P`1_3 |^2)*(R`3_3))
    -g2*gf1*(R`1_3*(R`3_3))*(P`3_3)*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
           +g2*(P`1_3 |^2)*(R`3_3))
    -g2*gf1*(P`3_3)*(R`1_3*(R`3_3))*(R`3_3)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
           by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3)
         +g2*(P`1_3 |^2)*(R`3_3))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3)*(R`3_3)*(g2*gf2*(P`2_3)
        -gf1*(P`1_3)) by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)
    *(P`3_3)*(R`1_3)+g2*(P`1_3 |^2)*(R`3_3))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3*(R`3_3))*(g2*gf2*(P`2_3)-gf1*(P`1_3))
           by GROUP_1:def 3
    .= -(g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3))+
        g2*(gf2 |^2)*(R`1_3)*(R`3_3)
    *(g2*(P`1_3 |^2)*(R`3_3)))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3*(R`3_3))*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by VECTSP_1:def 7
    .= -(g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g4*(P`1_3)*(P`3_3)*(R`1_3))
          +g2*(gf2 |^2)*(R`1_3)*(R`3_3)
    *(g2*(P`1_3 |^2)*(R`3_3)))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by EC_PF_1:22
    .= -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))*(g2*(P`1_3 |^2)*(R`3_3))
     -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by VECTSP_1:17
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*(g2*((P`1_3 |^2)*(R`3_3)))
    -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3)*(R`3_3)*g2*((P`1_3 |^2)*(R`3_3))
     -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(gf2 |^2)*(R`1_3*(R`3_3))*g2*((P`1_3 |^2)*(R`3_3))
   -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(gf2 |^2)*g2*(R`1_3*(R`3_3))*((P`1_3 |^2)*(R`3_3))
     -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*(gf2 |^2)*g2*((R`1_3*(R`3_3))*((P`1_3 |^2)*(R`3_3)))
     -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
         -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)
      -gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g2*g2*(gf2 |^2)*((R`1_3*(R`3_3))*((P`1_3 |^2)*(R`3_3)))
          -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g4*(gf2 |^2)*(R`1_3*(R`3_3)*(P`1_3 |^2)*(R`3_3))
           -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
          -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)
     -gf1*(P`1_3))
    by A4,GROUP_1:def 3
    .= -g4*(gf2 |^2)*(R`1_3*(P`1_3 |^2)*(R`3_3)*(R`3_3))
            -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
         -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)
           -gf1*(P`1_3))
    by GROUP_1:def 3
     .= -g4*(gf2 |^2)*(R`1_3*(P`1_3 |^2)*(R`3_3*(R`3_3)))
           -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -g4*(gf2 |^2)*(R`1_3*(P`1_3 |^2)*(R`3_3 |^2))
          -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by EC_PF_1:22
    .=  -g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3)*(R`3_3 |^2)
           -(g2*(gf2 |^2)*(R`1_3)*(R`3_3))
    *(g4*(P`1_3)*(P`3_3)*(R`1_3))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -g2*(gf2 |^2)*(R`1_3)*(R`3_3)
    *(g4*(P`1_3*(P`3_3)*(R`1_3)))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
          -g2*(gf2 |^2)*(R`1_3)*(R`3_3)
    *g4*(P`1_3*(P`3_3)*(R`1_3))
    -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
          -g2*(gf2 |^2)*(R`1_3*(R`3_3))
    *g4*(P`1_3*(P`3_3)*(R`1_3))
             -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -g2*(gf2 |^2)*g4*(R`1_3*(R`3_3))
    *(P`1_3*(P`3_3)*(R`1_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -g2*(gf2 |^2)*g4*((R`1_3*(R`3_3))
    *(P`1_3*(P`3_3)*(R`1_3)))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
            -g2*g4*(gf2 |^2)*((R`1_3*(R`3_3))
    *(P`1_3*(P`3_3)*(R`1_3)))
         -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
             -g8*(gf2 |^2)*(P`1_3*(P`3_3)*(R`1_3)
    *(R`1_3)*(R`3_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by A6,GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
               -g8*(gf2 |^2)*(P`1_3*(P`3_3)
    *(R`1_3*(R`1_3))*(R`3_3))
      -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
         -g8*(gf2 |^2)*(P`1_3*(P`3_3)
    *(R`1_3 |^2)*(R`3_3))
     -g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)-gf1*(P`1_3))
    by EC_PF_1:22
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2)*(R`3_3)-g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2)*(g2*gf2*(P`2_3)
         -gf1*(P`1_3))
    by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
  -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)
     -((g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(gf1*(P`1_3))) by VECTSP_1:11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
       -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(gf1*(P`1_3))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by VECTSP_1:17
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
      -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*gf1*(P`3_3*(R`1_3)*(R`3_3 |^2)))*(gf1*(P`1_3))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
      -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+(g2*gf1*(gf1*(P`1_3))*(P`3_3*(R`1_3)*(R`3_3 |^2))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
      -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+(g2*gf1*gf1*(P`1_3)*(P`3_3*(R`1_3)*(R`3_3 |^2))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
        -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+(g2*(gf1*gf1)*(P`1_3)*(P`3_3*(R`1_3)*(R`3_3 |^2))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
      -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+(g2*(gf1 |^2)*(P`1_3)*(P`3_3*(R`1_3)*(R`3_3 |^2))
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by EC_PF_1:22
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
              -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2)
    -(g2*gf1*(P`3_3)*(R`1_3)*(R`3_3 |^2))*(g2*gf2*(P`2_3))) by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
            -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g2*gf1*(P`3_3*(R`1_3)*(R`3_3 |^2)))*(g2*gf2*(P`2_3))) by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g2*gf1*(g2*gf2*(P`2_3))*(P`3_3*(R`1_3)*(R`3_3 |^2)))) by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g2*gf1*g2*gf2*(P`2_3)*(P`3_3*(R`1_3)*(R`3_3 |^2)))) by Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
           -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g2*g2*gf1*gf2*(P`2_3)*(P`3_3*(R`1_3)*(R`3_3 |^2)))) by GROUP_1:def 3
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
          -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)
    *(R`1_3 |^2))*(R`3_3)+((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))) by A4,Th11
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    +((g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
      -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2)))
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by ALGSTR_1:8
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
           -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by ALGSTR_1:7
    .= -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
               +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by ALGSTR_1:8;
    A9: -g4*(gf2 |^2)*(P`3_3 |^2)*(b*(R`3_3 |^3))
    = -g4*(gf2 |^2)*(P`3_3 |^2)*b*(R`3_3 |^(2+1)) by GROUP_1:def 3
    .= -g4*(gf2 |^2)*(P`3_3 |^2)*b*((R`3_3 |^2)*(R`3_3)) by EC_PF_1:24
    .= -g4*(gf2 |^2)*(P`3_3 |^2)*b*(R`3_3)*(R`3_3 |^2) by GROUP_1:def 3
    .= -(R`3_3 |^2)*(g4*(gf2 |^2)*(P`3_3 |^2)*(b*(R`3_3))) by GROUP_1:def 3
    .= -(R`3_3 |^2)*(R`3_3*((g2*gf2*(P`2_3)
      -gf1*(P`1_3)) |^2)-g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))
    by A1,A2,A3,Th61
    .= -((R`3_3 |^2)*(R`3_3*((g2*gf2*(P`2_3)-gf1*(P`1_3)) |^2))-(R`3_3 |^2)*
    (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))) by VECTSP_1:11
    .= (R`3_3 |^2)*(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))
    -(R`3_3 |^2)*(R`3_3*((g2*gf2*(P`2_3)-gf1*(P`1_3)) |^2)) by VECTSP_1:17
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(R`3_3 |^2)*(R`3_3)*((g2*gf2*(P`2_3)-gf1*(P`1_3)) |^2) by GROUP_1:def 3
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(R`3_3 |^(2+1))*((g2*gf2*(P`2_3)-gf1*(P`1_3)) |^2) by EC_PF_1:24
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    +(-(R`3_3 |^3))*((g2*gf2*(P`2_3)-gf1*(P`1_3)) |^2) by VECTSP_1:9
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(((g2*gf2*(P`2_3)) |^2)
           -g2*(g2*gf2*(P`2_3))*(gf1*(P`1_3))+((gf1*(P`1_3)) |^2))
    by A1,Th26
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *((g2 |^2)*(gf2 |^2)*(P`2_3 |^2)
    -g2*(g2*gf2*(P`2_3))*(gf1*(P`1_3))+((gf1*(P`1_3)) |^2))
    by Th13
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(g4*(gf2 |^2)*(P`2_3 |^2)
             -g2*(g2*gf2*(P`2_3))*(gf1*(P`1_3))+(gf1 |^2)*(P`1_3 |^2))
    by A5,BINOM:9
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(g4*(gf2 |^2)*(P`2_3 |^2)
      -g2*g2*gf2*(P`2_3)*(gf1*(P`1_3))+(gf1 |^2)*(P`1_3 |^2))
    by Th11
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(g4*(gf2 |^2)*(P`2_3 |^2)-g4*gf2*(gf1*(P`1_3))*(P`2_3)
      +(gf1 |^2)*(P`1_3 |^2))
    by A4,GROUP_1:def 3
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(g4*(gf2 |^2)*(P`2_3 |^2)
           -g4*gf2*gf1*(P`1_3)*(P`2_3)+(gf1 |^2)*(P`1_3 |^2))
    by GROUP_1:def 3
    .= (g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)+(-(R`3_3 |^3))
    *(g4*(gf2 |^2)*(P`2_3 |^2)
          -g4*gf1*gf2*(P`1_3)*(P`2_3)+(gf1 |^2)*(P`1_3 |^2))
    by GROUP_1:def 3
    .= g4*(gf2 |^2)*(P`2_3 |^2)*(-(R`3_3 |^3))
             -g4*gf1*gf2*(P`1_3)*(P`2_3)*(-(R`3_3 |^3))
    +(gf1 |^2)*(P`1_3 |^2)*(-(R`3_3 |^3))
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by Th14
    .= -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
             -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(-(R`3_3 |^3))
    +(gf1 |^2)*(P`1_3 |^2)*(-(R`3_3 |^3))
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by VECTSP_1:8
    .= -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
              -(-(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
    +(gf1 |^2)*(P`1_3 |^2)*(-(R`3_3 |^3))
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by VECTSP_1:8
    .= -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
           +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(gf1 |^2)*(P`1_3 |^2)*(-(R`3_3 |^3))
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by RLVECT_1:17
    .= -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
            +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    -(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by VECTSP_1:8;
    A10
: g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))-g4*(gf2 |^2)*(P`3_3 |^2)
    *(b*(R`3_3 |^3))
    = ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
           -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
    +g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^3)
     +(-(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
           +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2))) by A7,A9,ALGSTR_1:7
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
     -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
    +g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^3)
       -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3)
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by Th8
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
          -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
    +(g4*(gf2 |^2)*(P`2_3 |^2)*(R`3_3 |^3)
     -(g4*(gf2 |^2)*(P`2_3 |^2))*(R`3_3 |^3))
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by ALGSTR_1:7
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
          -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))+0.GF(p)
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by VECTSP_1:19
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by ALGSTR_1:7
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
    +(-(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3)
    +(g4*gf1*gf2*(P`1_3)*(P`2_3))*(R`3_3 |^3))
          +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by ALGSTR_1:7
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))+0.GF(p)
    +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by RLVECT_1:5
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
     +(-(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)) by ALGSTR_1:7
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
    -(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^3)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by ALGSTR_1:7
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    -(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^(2+1))
       +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by ALGSTR_1:8
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    -(gf1 |^2)*(P`1_3 |^2)*((R`3_3 |^2)*(R`3_3))
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by EC_PF_1:24
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)*(R`3_3)
    -(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^2)*(R`3_3)
     +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2) by GROUP_1:def 3
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)
    -(gf1 |^2)*(P`1_3 |^2)*(R`3_3 |^2))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
          +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by VECTSP_1:13
    .= ((gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)
          -(gf1 |^2)*((P`1_3 |^2)*(R`3_3 |^2)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= (gf1 |^2)*(((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)
    -(P`1_3 |^2)*(R`3_3 |^2))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by VECTSP_1:11
    .= (gf1 |^2)*(((P`3_3*(R`1_3)-P`1_3*(R`3_3)) |^2)
           -((P`1_3*(R`3_3)) |^2))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by BINOM:9
    .= (gf1 |^2)*(((P`3_3*(R`1_3)-P`1_3*(R`3_3))
             +P`1_3*(R`3_3))*((P`3_3*(R`1_3)-P`1_3*(R`3_3))
          -P`1_3*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by Th15
    .= (gf1 |^2)*((P`3_3*(R`1_3)-P`1_3*(R`3_3)
     +P`1_3*(R`3_3))*(P`3_3*(R`1_3)-(P`1_3*(R`3_3)+P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
     +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by VECTSP_1:17
    .= (gf1 |^2)*((P`3_3*(R`1_3)+(-P`1_3*(R`3_3)+P`1_3*(R`3_3)))*(P`3_3*(R`1_3)
    -(P`1_3*(R`3_3)+P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by ALGSTR_1:7
    .= (gf1 |^2)*((P`3_3*(R`1_3)+0.GF(p))*(P`3_3*(R`1_3)
    -(P`1_3*(R`3_3)+P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by RLVECT_1:5
    .= (gf1 |^2)*((P`3_3*(R`1_3)+0.GF(p))*(P`3_3*(R`1_3)
          -g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by A1,Th20
    .= (gf1 |^2)*((P`3_3*(R`1_3))*(P`3_3*(R`1_3)-g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by RLVECT_1:4
    .= (gf1 |^2)*(P`3_3*(R`1_3))*(P`3_3*(R`1_3)-g2*(P`1_3*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3*(R`1_3))*(P`3_3*(R`1_3))
    -(gf1 |^2)*(P`3_3*(R`1_3))*(g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by VECTSP_1:11
    .= ((gf1 |^2)*((P`3_3*(R`1_3))*(P`3_3*(R`1_3)))
    -(gf1 |^2)*(P`3_3*(R`1_3))*(g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*((P`3_3*(R`1_3)) |^2)
   -(gf1 |^2)*(P`3_3*(R`1_3))*(g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
   +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by EC_PF_1:22
    .= ((gf1 |^2)*((P`3_3 |^2)*(R`1_3 |^2))
   -(gf1 |^2)*(P`3_3*(R`1_3))*(g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by BINOM:9
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
     -(gf1 |^2)*(P`3_3*(R`1_3))*(g2*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
     -(gf1 |^2)*(P`3_3*(R`1_3))*g2*(P`1_3*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
    -(gf1 |^2)*g2*(P`3_3*(R`1_3))*(P`1_3*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
    -g2*(gf1 |^2)*((P`3_3*(R`1_3))*(P`1_3*(R`3_3))))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
    -g2*(gf1 |^2)*((P`3_3*(R`1_3))*(P`1_3)*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
       -g2*(gf1 |^2)*(P`1_3*(P`3_3)*(R`1_3)*(R`3_3)))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)
    -g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3)*(R`3_3))*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by Th11
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
    -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3)*(R`3_3)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
          +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by VECTSP_1:13
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
          -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3*(R`3_3))
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
          +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by GROUP_1:def 3
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
      -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    by EC_PF_1:22;
    A11
: g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))-g4*(gf2 |^2)*(P`3_3 |^2)
    *(a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3))
    = g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))-(g4*(gf2 |^2)*(P`3_3 |^2)
    *(a*(R`1_3)*(R`3_3 |^2))+g4*(gf2 |^2)*(P`3_3 |^2)*(b*(R`3_3 |^3)))
        by VECTSP_1:def 7
    .= g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))-g4*(gf2 |^2)*(P`3_3 |^2)
    *(b*(R`3_3 |^3))-g4*(gf2 |^2)*(P`3_3 |^2)*(a*(R`1_3)*(R`3_3 |^2))
     by VECTSP_1:17
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
   -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
    +(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by A8,A10,Th8
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
    -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
    +((g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2)
    -(g4*(gf2 |^2)*(P`1_3 |^2)*(R`1_3))*(R`3_3 |^2))
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by ALGSTR_1:7
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
     -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))+0.GF(p)
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
     +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by RLVECT_1:5
    .= ((gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
     -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2))
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by RLVECT_1:4
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
     -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +((g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g4*gf1*gf2*(P`2_3)*(P`3_3)*(R`1_3)*(R`3_3 |^2)))
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by ALGSTR_1:7
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
     -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +0.GF(p)+(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by RLVECT_1:5
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
     -(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
   -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3)
    by RLVECT_1:4
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
          +(-(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2)
    +(g2*(gf1 |^2)*(P`1_3)*(P`3_3)*(R`1_3))*(R`3_3 |^2))
      -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3)
    by ALGSTR_1:7
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)+0.GF(p)
    -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3) by RLVECT_1:5
    .= (gf1 |^2)*(P`3_3 |^2)*(R`1_3 |^2)*(R`3_3)
          -(g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2))*(R`3_3)
    by RLVECT_1:4
    .= (gf1 |^2)*(P`3_3 |^2)*((R`1_3 |^2)*(R`3_3))
          -g8*(gf2 |^2)*(P`1_3)*(P`3_3)*(R`1_3 |^2)*(R`3_3)
    by GROUP_1:def 3
    .= (gf1 |^2)*(P`3_3 |^2)*((R`1_3 |^2)*(R`3_3))
               -g8*(gf2 |^2)*(P`1_3)*(P`3_3)*((R`1_3 |^2)*(R`3_3))
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3 |^2)
     -g8*(gf2 |^2)*(P`1_3)*(P`3_3))*((R`1_3 |^2)*(R`3_3))
    by VECTSP_1:13
    .= ((gf1 |^2)*(P`3_3*(P`3_3))
            -g8*(gf2 |^2)*(P`1_3)*(P`3_3))*((R`1_3 |^2)*(R`3_3))
    by EC_PF_1:22
     .= ((gf1 |^2)*(P`3_3*(P`3_3))
         -g8*(gf2 |^2)*(P`1_3)*(P`3_3))*(R`1_3 |^2)*(R`3_3)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3)*(P`3_3)
       -g8*(gf2 |^2)*(P`1_3)*(P`3_3))*(R`1_3 |^2)*(R`3_3)
    by GROUP_1:def 3
    .= ((gf1 |^2)*(P`3_3)-g8*(gf2 |^2)*(P`1_3))*(P`3_3)*(R`1_3 |^2)*(R`3_3)
   by VECTSP_1:13
    .= R`3_3*((gf1 |^2)*(P`3_3)-g8*(gf2 |^2)*(P`1_3))*(P`3_3)*(R`1_3 |^2)
        by Th11
    .= g4*(gf2 |^2)*(P`3_3)*(R`1_3)*(P`3_3)*(R`1_3 |^2) by A1,A2,A3,Th60
    .= g4*(gf2 |^2)*(P`3_3)*(P`3_3)*(R`1_3)*(R`1_3 |^2) by GROUP_1:def 3
    .= g4*(gf2 |^2)*(P`3_3*(P`3_3))*(R`1_3)*(R`1_3 |^2) by GROUP_1:def 3
    .= g4*(gf2 |^2)*(P`3_3 |^2)*(R`1_3)*(R`1_3 |^2) by EC_PF_1:22
    .= g4*(gf2 |^2)*(P`3_3 |^2)*((R`1_3 |^2)*(R`1_3)) by GROUP_1:def 3
    .= g4*(gf2 |^2)*(P`3_3 |^2)*(R`1_3 |^(2+1)) by EC_PF_1:24
    .= g4*(gf2 |^2)*(P`3_3 |^2)*(R`1_3 |^3);
    thus g4*(gf2 |^2)*(P`3_3 |^2)*
    ((R`2_3 |^2)*(R`3_3)-((R`1_3 |^3)+a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3)))
    = g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))
    -g4*(gf2 |^2)*(P`3_3 |^2)*((R`1_3 |^3)+a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3))
    by VECTSP_1:11
    .= g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))
    -g4*(gf2 |^2)*(P`3_3 |^2)*((R`1_3 |^3)
          +(a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3)))
    by ALGSTR_1:7
    .= g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))
    -(g4*(gf2 |^2)*(P`3_3 |^2)*(R`1_3 |^3)+g4*(gf2 |^2)*(P`3_3 |^2)
    *(a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3))) by VECTSP_1:def 7
    .= g4*(gf2 |^2)*(P`3_3 |^2)*((R`2_3 |^2)*(R`3_3))
    -g4*(gf2 |^2)*(P`3_3 |^2)*(a*(R`1_3)*(R`3_3 |^2)+b*(R`3_3 |^3))
    -g4*(gf2 |^2)*(P`3_3 |^2)*(R`1_3 |^3) by VECTSP_1:17
    .= 0.GF(p) by A11,RLVECT_1:5;
  end;
