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

theorem
  a <= b"\/"c implies a\b <= c & a\c <= b
proof
  assume
A1: a <= b"\/"c;
  (b"\/"c)"/\" 'not' b = ('not' b"/\"b) "\/" ('not' b"/\"c) by WAYBEL_1:def 3
    .= Bottom L "\/" ('not' b"/\"c) by Th34
    .= c"/\"'not' b by WAYBEL_1:3;
  then c"/\"'not' b <= c & a"/\"'not' b <= c"/\"'not' b by A1,Th6,YELLOW_0:23;
  hence a\b <= c by YELLOW_0:def 2;
  (b"\/"c)"/\" 'not' c = ('not' c"/\"b) "\/" ('not' c"/\" c) by WAYBEL_1:def 3
    .= ('not' c"/\"b)"\/" Bottom L by Th34
    .= 'not' c"/\"b by WAYBEL_1:3;
  then 'not' c"/\"b <= b & a"/\"'not' c <= 'not' c"/\"b by A1,Th6,YELLOW_0:23;
  hence thesis by YELLOW_0:def 2;
end;
