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
  f c= g implies max(f,g) = g
proof
  assume f c= g;
  then
A1: max(f,g) c= g by Th18;
  g c= max(f,g) by Th16;
  hence thesis by A1,Lm1;
end;
