theorem
  for a,b,x,y being Real st a > 0 & x < y holds AffineMap(a,b).x
  < AffineMap(a,b).y
proof
  let a,b,x,y be Real;
  assume a > 0 & x < y;
  then
A1: a*x < a*y by XREAL_1:68;
  AffineMap(a,b).x = a*x + b & AffineMap(a,b).y = a*y + b by Def4;
  hence thesis by A1,XREAL_1:8;
end;
