reserve n,n1,n2,m for Nat;
reserve r,g1,g2,g,g9 for Complex;
reserve R,R2 for Real;
reserve s,s9,s1 for Complex_Sequence;

theorem
  (s9/"s)*' = (s9*') /" (s*')
proof
  now
    let n be Element of NAT;
    thus (s9/"s)*'.n = ((s9 (#) s").n)*' by Def2
      .= ((s9.n) * (s".n))*' by VALUED_1:5
      .= ((s9.n) * (s.n)")*' by VALUED_1:10
      .= (s9.n)*' * ((s.n)")*' by COMPLEX1:35
      .= (s9.n)*' * ((s.n)*')" by COMPLEX1:36
      .= (s9*').n * ((s.n)*')" by Def2
      .= (s9*').n * ((s*').n)" by Def2
      .= (s9*').n * ((s*')").n by VALUED_1:10
      .= ((s9*') /" (s*')).n by VALUED_1:5;
  end;
  hence thesis by FUNCT_2:63;
end;
