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
  max(h,h) = h & min(h,h) = h & max(h,h) = min(h,h) & min(f,g) = min(g,f
  ) & max(f,g) = max(g,f);
