reserve a,b,r for non unit non zero Real;

theorem Th01:
  op2(op1(r)) = (r - 1) / r &
  op1(op2(r)) = 1 / (1 - r) &
  op1(op2(op1(r))) = r / (r - 1) &
  op2(op1(op2(r))) = r / (r - 1)
  proof
A1: 1 - 1 / r = r / r - 1 / r by XCMPLX_1:60
             .= (r - 1) / r;
    1 - r <> 0 by Def01;
    then 1 - (1 / (1 - r)) = ((1 - r) / (1 - r)) - 1 / (1 - r) by XCMPLX_1:60
                          .= -r / (1 - r)
                          .= r / -(1 - r) by XCMPLX_1:188;
    hence thesis by A1,XCMPLX_1:57;
  end;
