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_1:65;
  AffineMap(a,b).x = a*x + b & AffineMap(a,b).y = a*y + b by Def4;
  hence thesis by A1,XREAL_1:7;
end;
