theorem Th26:
  f=F & f|X is bounded implies |.f.x.| <= ||.F.||
proof
  assume that
A1: f=F and
A2: f|X is bounded;
A3: |.f.x.| in PreNorms f;
  PreNorms f is non empty bounded_above by A2,Th17;
  then |.f.x.| <= upper_bound PreNorms f by A3,SEQ_4:def 1;
  hence thesis by A1,A2,Th20;
end;
