
theorem
  for L be lower-bounded LATTICE for a,b,c be Element of L holds a <= b
  & a <= c & b misses c implies a = Bottom L
proof
  let L be lower-bounded LATTICE;
  let a,b,c be Element of L;
  assume that
A1: a <= b and
A2: a <= c and
A3: b misses c;
  b"/\"c = Bottom L by A3;
  then Bottom L <= a"/\"c & a"/\"c <= Bottom L by A1,Th6,YELLOW_0:44;
  then a"/\"c = Bottom L by YELLOW_0:def 3;
  hence thesis by A2,Th10;
end;
