
theorem Th34:
  for L being non empty RelStr, x being Element of [:L,L:] holds (
  sup_op L).x = x`1 "\/" x`2
proof
  let L be non empty RelStr, x be Element of [:L,L:];
  the carrier of [:L,L:] = [:the carrier of L, the carrier of L:] by
YELLOW_3:def 2;
  then
  ex a, b being object st a in the carrier of L & b in the carrier of L & x =
  [a,b] by ZFMISC_1:def 2;
  hence (sup_op L).x = (sup_op L).(x`1,x`2)
    .= x`1 "\/" x`2 by Def5;
end;
