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);

theorem Th22:
  x,x Fr_Eq S
  proof
    reconsider s1 = 1.R as Element of R;
A1: (x`1 * x`2 - x`1 * x`2) * s1 = 0.R by VECTSP_1:19;
    s1 in S by C0SP1:def 4;
    hence thesis by A1;
  end;
