reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;

theorem
  Sum<* - v,- v *> = (-(1r+1r)) * v
proof
  reconsider 2r = 2+0*<i> as Element of COMPLEX by XCMPLX_0:def 2;
  thus Sum<* - v,- v *> = - (v + v) by RLVECT_1:60
    .= - Sum<* v,v *> by RLVECT_1:45
    .= - ((1r+1r) * v) by Th17
    .= (- 1r) * (2r * v) by Th3
    .= ((- 1r) * 2r) * v by Def4
    .= (-(1r+1r)) * v;
end;
