reserve x for object, X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for complex-valued Function;
reserve r,p for Complex;
reserve r,r1,r2,p for Real;
reserve f,f1,f2 for PartFunc of C,REAL;
reserve f for real-valued Function;
reserve f1,f2 for real-valued Function;
reserve f,f1,f2 for PartFunc of C,REAL;

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;
