
theorem Th24:
  for L being with_infima with_suprema PartialOrdered non empty
OrthoRelStr for x,y being Element of L holds x <= y implies y = x "|_|" y & x
  = x "|^|" y
proof
  let L be with_infima with_suprema PartialOrdered non empty OrthoRelStr;
  let a,b be Element of L;
  assume
A1: a <= b;
  then b = b "|_|" a by YELLOW_0:24;
  hence thesis by A1,LATTICE3:13,YELLOW_0:25;
end;
