theorem
  f|Y is constant implies (for r holds (r(#)f)|Y is bounded) & (-f)|Y is
  bounded & (abs f)|Y is bounded
proof
  assume
A1: f|Y is constant;
  hereby
    let r;
    (r(#)f)|Y is constant by A1,Th89;
    hence (r(#)f)|Y is bounded;
  end;
  (-f)|Y is constant by A1,Th90;
  hence (-f)|Y is bounded;
  (abs f)|Y is constant by A1,Th91;
  hence thesis;
end;
