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