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)*;
reserve SM for monotone OrderSortedSign,
  o,o1,o2 for OperSymbol of SM,
  w1 for Element of (the carrier of SM)*;
reserve SR for regular monotone OrderSortedSign,
  o,o1,o3,o4 for OperSymbol of SR,
  w1 for Element of (the carrier of SR)*;
reserve R for non empty Poset;
reserve z for non empty set;
reserve s1,s2 for SortSymbol of S,
  o,o1,o2,o3 for OperSymbol of S,
  w1,w2 for Element of (the carrier of S)*;
reserve CH for ManySortedFunction of ConstOSSet(S,z)# * the Arity of S,
  ConstOSSet(S,z) * the ResultSort of S;
reserve A for OSAlgebra of S;
reserve M for MSAlgebra over S0;
reserve A for OSAlgebra of S;
reserve op1,op2 for OperSymbol of S;

theorem Th33:
  for on being OperName of S, op being OperSymbol of S holds op is
  Element of on iff Name op = on
proof
  let on be OperName of S, op1 be OperSymbol of S;
  hereby
    assume op1 is Element of on;
    then reconsider op = op1 as Element of on;
    (ex op2 being object st op2 in the carrier' of S & on = Class (the
Overloading of S,op2) )& Name op = Class(the Overloading of S,op) by
EQREL_1:def 3;
    hence Name op1 = on by EQREL_1:23;
  end;
  assume Name op1 = on;
  hence thesis by EQREL_1:20;
end;
