theorem
  0.R in S implies x,y Fr_Eq S
  proof
    assume
A1: 0.R in S;
    reconsider s1 = 0.R as Element of R;
A2: (x`1 * y`2 - y`1 * x`2) * s1 = 0.R;
    reconsider s1 as Element of S by A1;
    thus thesis by A1,A2;
  end;
