reserve A for non empty closed_interval Subset of REAL;

theorem
  for a,x be Real holds a - |. a*x .| <= a
proof
  let a,x be Real;
  |. a*x .| >= 0 by COMPLEX1:46; then
  -|. a*x .| +a <= 0+a by XREAL_1:6;
  hence thesis;
end;
