reserve i,j,n,n1,n2,m,k,l,u for Nat,
        r,r1,r2 for Real,
        x,y for Integer,
        a,b for non trivial Nat,
        F for XFinSequence,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;

theorem Th9:
  c1 + <%c2%> = <%c1 + c2%>
  proof
A1:   dom <%c1 + c2%> = 1 = dom <%c2%> = dom (c1 + <%c2%>)
      by VALUED_1:def 2,AFINSQ_1:def 4;
    <%c1 + c2%>.0 = c1+(<%c2%>.0)
      .= (c1 + <%c2%>).0 by A1,AFINSQ_1:66,VALUED_1:def 2;
    hence thesis by A1,AFINSQ_1:def 4;
  end;
