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

theorem
  a misses b implies (a"\/"b)\b = a
proof
  assume a misses b;
  then a"/\"b = Bottom L;
  then (a"\/"'not' b)"/\"(b"\/"'not' b) <= Bottom L "\/"'not' b by Th17;
  then (a"\/"'not' b)"/\"(b"\/"'not' b) <= 'not' b by WAYBEL_1:3;
  then (a"\/"'not' b)"/\"Top L <= 'not' b by Th34;
  then
A1: a"\/"'not' b <= 'not' b by WAYBEL_1:4;
  'not' b <= a"\/"'not' b by YELLOW_0:22;
  then a"\/"'not' b = 'not' b by A1,YELLOW_0:def 3;
  then
A2: a <= 'not' b by YELLOW_0:22;
  (a"\/"b)\b = (a"\/"b)"/\"'not' b
    .= (a"/\"'not' b)"\/"(b"/\"'not' b) by WAYBEL_1:def 3
    .= (a"/\"'not' b)"\/"Bottom L by Th34
    .= a"/\"'not' b by WAYBEL_1:3
    .= a by A2,Th10;
  hence thesis;
end;
