theorem Th30:
  for s be Element of S holds
    x=[s,s] implies x,1.(R,S) Fr_Eq S
   proof
     let s be Element of S;
     assume
A1:  x=[s,s];
     reconsider s1 = 1.R as Element of R;
A2:  (x`1 * 1.(R,S)`2 - 1.(R,S)`1 * x`2)*s1 = 0.R by A1,RLVECT_1:5;
     s1 in S by C0SP1:def 4;
     hence thesis by A2;
   end;
