theorem
  X c= dom f1 /\ dom f2 & f1|X is continuous & f1"{0} = {} & f2|X is
  continuous implies (f2/f1)|X is continuous
proof
  assume
A1: X c= dom f1 /\ dom f2;
  assume that
A2: f1|X is continuous and
A3: f1"{0} = {} and
A4: f2|X is continuous;
A5: dom(f1^) = dom f1 \ {} by A3,RFUNCT_1:def 2
    .= dom f1;
  (f1^)|X is continuous by A2,A3,Th22;
  then (f2(#)(f1^))|X is continuous by A1,A4,A5,Th18;
  hence thesis by RFUNCT_1:31;
end;
