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

theorem
  a"/\"(b\c) = a"/\"b \ a"/\"c
proof
  thus a"/\"b \ a"/\"c = (a"/\"b) "/\"('not' a"\/"'not' c) by Th36
    .= ((a"/\"b)"/\"'not' a)"\/"((a"/\"b)"/\" 'not' c) by WAYBEL_1:def 3
    .= ((a"/\"'not' a)"/\"b)"\/"((a"/\"b)"/\" 'not' c) by LATTICE3:16
    .= (Bottom L"/\"b)"\/"((a"/\"b)"/\"'not' c) by Th34
    .= Bottom L"\/"((a"/\"b)"/\"'not' c) by WAYBEL_1:3
    .= (a"/\"b)"/\"'not' c by WAYBEL_1:3
    .= a"/\"(b\c) by LATTICE3:16;
end;
