theorem Th7:
  A is complex-containing & (for d holds a is_complex_on d)
  implies for d holds a is_a_value_on d
  proof
    assume that
A1: COMPLEX c= A and
A2: for d holds a is_complex_on d;
    let d;
    a is_complex_on d by A2;
    then denaming(V,A,a).d in COMPLEX by XCMPLX_0:def 2;
    hence denaming(V,A,a).d in A by A1;
  end;
