 reserve a,b,c,x for Real;

theorem Cb1:
  c - b <> 0 implies
    AffineMap (-1/(c-b),c/(c-b)).b = 1
  proof
    assume
A1: c - b <> 0;
    AffineMap (-1/(c-b),c/(c-b)).b
         = (-1/(c-b))*b+c/(c-b) by FCONT_1:def 4
        .= ((-1)/(c-b))*b+c/(c-b) by XCMPLX_1:187
        .= (((-1)*b)/(c-b))+c/(c-b) by XCMPLX_1:74
        .= (-b+c)/(c-b) by XCMPLX_1:62
        .= 1 by A1,XCMPLX_1:60;
    hence thesis;
  end;
