 reserve a,b,c,x for Real;

theorem Ah1:
  AffineMap (1/(b-a),-a/(b-a)).a = 0
  proof
    AffineMap (1/(b-a),-a/(b-a)).a = (1/(b-a))*a+-a/(b-a) by FCONT_1:def 4
        .= (1/(b-a))*a+(-a)/(b-a) by XCMPLX_1:187
        .= (1/(b-a))*a+a*((-1))/(b-a)
        .= a*(1/(b-a))+a*((-1)/(b-a)) by XCMPLX_1:74
        .= a*(1/(b-a)+(-1)/(b-a))
        .= a*(1/(b-a)+-1/(b-a)) by XCMPLX_1:187
        .= 0;
    hence thesis;
  end;
