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

theorem
  a"/\"b = Bottom L iff a\b = a
proof
  thus a"/\"b = Bottom L implies a\b = a
  proof
    assume a"/\"b = Bottom L;
    then a <= 'not' b by WAYBEL_1:82;
    then a"/\"a <= a"/\"'not' b by Th6;
    then
A1: a <= a"/\"'not' b by Th2;
    a\b <= a by YELLOW_0:23;
    hence thesis by A1,YELLOW_0:def 3;
  end;
  thus a\b = a implies a"/\"b = Bottom L
  proof
    assume a\b = a;
    then 'not' a"\/"'not' 'not' b = 'not' a by Th36;
    then a"/\"('not' a"\/"b) <= a"/\"'not' a by WAYBEL_1:87;
    then (a"/\"'not' a)"\/"(a"/\"b) <= a"/\"'not' a by WAYBEL_1:def 3;
    then Bottom L"\/"(a"/\"b) <= a"/\"'not' a by Th34;
    then Bottom L"\/"(a"/\"b) <= Bottom L by Th34;
    then
A2: a"/\"b <= Bottom L by WAYBEL_1:3;
    Bottom L <= a"/\"b by YELLOW_0:44;
    hence thesis by A2,YELLOW_0:def 3;
  end;
end;
