
theorem Th20:
  for S, T being antisymmetric up-complete non empty reflexive
RelStr, x, y being Element of [:S,T:] st x << y holds x`1 << y`1 & x`2 << y`2
proof
  let S, T be antisymmetric up-complete non empty reflexive RelStr, x, y be
  Element of [:S,T:] such that
A1: x << y;
  the carrier of [:S,T:] = [:the carrier of S,the carrier of T:] by
YELLOW_3:def 2;
  then x = [x`1,x`2] & y = [y`1,y`2] by MCART_1:21;
  hence thesis by A1,Th18;
end;
