theorem Th73:
  f|Y is bounded implies |.f.||Y is bounded & (-f)|Y is bounded
proof
  assume
A1: f|Y is bounded;
  |.f.||Y = |.f|Y.| by RFUNCT_1:46;
  hence |.f.||Y is bounded by A1,Lm3;
  thus thesis by A1,Th71;
end;
