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,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;
