 reserve a,b,c,x for Real;

theorem Ab1:
  b - a <> 0 implies
    AffineMap (1/(b-a),-a/(b-a)).b = 1
  proof
    assume
A1: b - a <> 0;
    AffineMap (1/(b-a),-a/(b-a)).b = (1/(b-a))*b+-a/(b-a) by FCONT_1:def 4
        .= (b/(b-a))+-a/(b-a) by XCMPLX_1:99
        .= (b/(b-a))+(-a)/(b-a) by XCMPLX_1:187
        .= (b+-a)/(b-a) by XCMPLX_1:62
        .= (1/(b-a))*(b+-a) by XCMPLX_1:99
        .= 1 by XCMPLX_1:106,A1;
    hence thesis;
  end;
