theorem
  min(f,g) c= max(f,g)
proof
  let x be Element of C;
  min(f.x,g.x) <= f.x & f.x <= max(f.x,g.x) by XXREAL_0:17,25;
  then min(f.x,g.x) <= max(f.x,g.x) by XXREAL_0:2;
  then min(f.x,g.x) <= max(f,g).x by Def4;
  hence thesis by Def3;
end;
