theorem Th50:
  for a,b being Real st a<> 0 holds AffineMap(a,b) is one-to-one
proof
  let a,b be Real such that
A1: a<> 0;
  let x1,x2 be object;
  set f = AffineMap(a,b);
  assume x1 in dom f;
  then reconsider r1 = x1 as Real;
  assume x2 in dom f;
  then reconsider r2 = x2 as Real;
  assume f.x1 = f.x2;
  then a*r1+b = f.x2 by Def4
    .= a*r2 +b by Def4;
  hence thesis by A1,XCMPLX_1:5;
end;
