
theorem Th6: :: Sym0:
for R being symmetric RelStr, x, y being Element of R st x <= y holds y <= x
proof
 let R be symmetric RelStr, x, y be Element of R; assume
A1: x <= y;
   set cR = the carrier of R, iR = the InternalRel of R;
A2: iR is_symmetric_in cR by NECKLACE:def 3;
A3: [x,y] in iR by A1,ORDERS_2:def 5;
   then x in cR & y in cR by ZFMISC_1:87;
   then [y,x] in iR by A2,A3;
 hence y <= x by ORDERS_2:def 5;
end;
