
theorem
  for L be lower-bounded antisymmetric transitive with_infima RelStr for
  a,b,c be Element of L holds a misses c & b <= c implies a misses b
proof
  let L be lower-bounded antisymmetric transitive with_infima RelStr;
  let a,b,c be Element of L;
  assume that
A1: a misses c and
A2: b <= c;
  a"/\"c = Bottom L by A1;
  then
A3: a"/\"b <= Bottom L by A2,Th6;
  Bottom L <= a"/\"b by YELLOW_0:44;
  then a"/\"b = Bottom L by A3,YELLOW_0:def 3;
  hence thesis;
end;
