reserve x,y,y1,y2 for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,h,g,h1 for Membership_Func of C;

theorem Th16:
  min(f,g) c= f & f c= max(f,g)
proof
  thus min(f,g) c= f
  proof
    let x be Element of C;
    min(f,g).x = min(f.x,g.x) by Def3;
    hence thesis by XXREAL_0:17;
  end;
  let x be Element of C;
  max(f,g).x = max(f.x,g.x) by Def4;
  hence thesis by XXREAL_0:25;
end;
