reserve A,O for non empty set,
  R for Order of A,
  Ol for Equivalence_Relation of O,
  f for Function of O,A*,
  g for Function of O,A;
reserve S for OverloadedRSSign;
reserve S0 for non empty non void ManySortedSign;

theorem Th5:
  OSSign S0 is discrete op-discrete
proof
  set s = OSSign S0;
  set ol = the Overloading of s;
  the carrier of S0 = the carrier of OSSign S0 & id the carrier of S0 =
  the InternalRel of OSSign S0 by Def5;
  hence OSSign S0 is discrete by ORDERS_3:def 1;
  the Overloading of OSSign S0 = id the carrier' of S0 by Def5;
  then for x,y be OperSymbol of s st x ~= y holds x = y by RELAT_1:def 10;
  hence thesis by Th3;
end;
