theorem Th9:
  S is op-discrete implies S is monotone
proof
  set ol = the Overloading of S;
  assume S is op-discrete;
  then
A1: ol = id the carrier' of S;
  let o be OperSymbol of S;
  let o2 be OperSymbol of S;
  assume o ~= o2;
  then [o,o2] in ol;
  hence thesis by A1,RELAT_1:def 10;
end;
