reserve L for Boolean non empty RelStr;
reserve a,b,c,d for Element of L;

theorem
  a\b = Bottom L iff a <= b
proof
  thus a\b = Bottom L implies a <= b
  proof
    assume a\b = Bottom L;
    then (b"\/"a) "/\" (b "\/" 'not' b) <= b "\/"Bottom L by Th17;
    then (b"\/"a) "/\" (b "\/" 'not' b) <= b by WAYBEL_1:3;
    then (a"\/"b) "/\" Top L <= b by Th34;
    then
A1: a"\/"b <= b by WAYBEL_1:4;
    a <= a "\/" b by YELLOW_0:22;
    hence thesis by A1,YELLOW_0:def 2;
  end;
  thus a <= b implies a\b = Bottom L
  proof
    assume a <= b;
    then a "/\" 'not' b <= b "/\"'not' b by Th6;
    then
A2: a "/\" 'not' b <= Bottom L by Th34;
    Bottom L <= a\b by YELLOW_0:44;
    hence thesis by A2,YELLOW_0:def 3;
  end;
end;
