theorem
  Sum<* v,v,v *> = (1r+1r+1r) * v
proof
  reconsider 2r = 2+0*<i> as Element of COMPLEX by XCMPLX_0:def 2;
  thus Sum<* v,v,v *> = Sum<* v,v *> + v by RLVECT_1:66
    .= (1r+1r) * v + v by Th17
    .= (1r+1r) * v + 1r * v by Def5
    .= (1r+1r+1r) * v by Def3;
end;
