reserve R,R1 for commutative Ring;
reserve A,B for non degenerated commutative Ring;
reserve o,o1,o2 for object;
reserve r,r1,r2 for Element of R;
reserve a,a1,a2,b,b1 for Element of A;
reserve f for Function of R, R1;
reserve p for Element of Spectrum A;
reserve S for non empty multiplicatively-closed Subset of R;
reserve u,v,w,x,y,z for Element of Frac(S);
reserve a, b, c for Element of Frac(S);
reserve x, y, z for Element of S~R;

theorem Th32:
  for x holds
   ex a being Element of Frac(S) st x = Class(EqRel(S),a)
   proof
     let x;
     the carrier of S~R = Class EqRel(S) by Def6; then
     x in Class EqRel(S); then
     ex a being object st a in Frac(S) & x = Class(EqRel(S),a)
     by EQREL_1:def 3;
     hence thesis;
   end;
