
theorem Th7:
  for O being OrderInvolutive PartialOrdered non empty OrthoRelStr
  , x, y being Element of O holds x <= y implies y` <= x`
proof
  let O be OrderInvolutive PartialOrdered non empty OrthoRelStr, x, y be
  Element of O;
  assume
A1: x <= y;
  consider f being Function of O,O such that
A2: f = the Compl of O and
A3: f is Orderinvolutive by OPOSET_1:def 18;
  f is involutive antitone by A3,OPOSET_1:def 17;
  then f.x >= f.y by A1,WAYBEL_9:def 1;
  then x` >= f.y by A2,ROBBINS1:def 3;
  hence thesis by A2,ROBBINS1:def 3;
end;
