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 Th20:
  Fracmult(x,Fracmult(y,z)) = Fracmult(Fracmult(x,y),z)
  proof
    [x`1*(y`1*z`1),x`2*(y`2*z`2)]
    = [x`1*(y`1*z`1),(x`2*y`2)*z`2] by GROUP_1:def 3
    .= Fracmult(Fracmult(x,y),z) by GROUP_1:def 3;
    hence thesis;
  end;
