
theorem
  for L be lower-bounded antisymmetric transitive with_infima RelStr for
  a,b,c be Element of L holds a misses b implies (a"/\"c) misses (b"/\"c)
proof
  let L be lower-bounded antisymmetric transitive with_infima RelStr;
  let a,b,c be Element of L;
  assume
A1: a misses b;
  (a"/\"c)"/\"(b"/\"c) = c"/\"(a"/\"(b"/\"c)) by LATTICE3:16
    .= c"/\"(a"/\"b)"/\"c by LATTICE3:16
    .= c"/\"Bottom L"/\"c by A1
    .= Bottom L"/\"c by Th25
    .=Bottom L by Th25;
  hence thesis;
end;
