theorem
  for X being set holds X is OperName of S iff ex op1 st X = Name op1
proof
  let X be set;
  hereby
    assume X is OperName of S;
    then consider x being object such that
A1: x in the carrier' of S and
A2: X = Class(the Overloading of S,x) by EQREL_1:def 3;
    reconsider x1 = x as OperSymbol of S by A1;
    take x1;
    thus X = Name x1 by A2;
  end;
  given op1 such that
A3: X = Name op1;
  thus thesis by A3;
end;
