theorem Th80:
  f|Y is constant implies f|Y is bounded
proof
  assume f|Y is constant;
  then consider r being Element of COMPLEX such that
A1: for c st c in Y /\ dom f holds (f/.c) = r by PARTFUN2:35;
  now
    take p=|.r.|;
    let c;
    assume c in Y /\ dom f;
    hence |.(f/.c).| <= p by A1;
  end;
  hence thesis by Th68;
end;
