reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem Th21:
  x0<>x1 implies [!AffineMap(a,b),x0,x1!] = a
proof
  assume x0<>x1;
  then
A1: x0-x1<>0;
  [!AffineMap(a,b),x0,x1!] = (a*x0+b-AffineMap(a,b).x1)/(x0-x1)
      by FCONT_1:def 4
    .= (a*x0+b-(a*x1+b))/(x0-x1) by FCONT_1:def 4
    .= a*(x0-x1)/(x0-x1);
  hence thesis by A1,XCMPLX_1:89;
end;
