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;
reserve S for non empty Poset;
reserve s1,s2 for Element of S;
reserve w1,w2 for Element of (the carrier of S)*;
reserve S for OrderSortedSign;
reserve o,o1,o2 for OperSymbol of S;
reserve w1 for Element of (the carrier of S)*;

theorem :: constants not overloaded if monotone
  S is monotone & the_arity_of o1 = {} & o1 ~= o2 & the_arity_of o2 = {}
  implies o1=o2
proof
  assume that
A1: S is monotone and
A2: the_arity_of o1 = {} & o1 ~= o2 & the_arity_of o2 = {};
  the_result_sort_of o1 <= the_result_sort_of o2 & the_result_sort_of o2
  <= the_result_sort_of o1 by A1,A2,Def7;
  then the_result_sort_of o1 = the_result_sort_of o2 by ORDERS_2:2;
  hence thesis by A2,Def3;
end;
