Factually inaccurate. Apple did not sue Woolworths. Apple registered an objection against the granting of Woolworth's trademark during the period that the granting agency (IP Australia) specifically asks for objections to be filed.

From Wikipedia's entry on Australian trademark law: If an application is accepted it will be published for opposition purposes for three months, during which time third parties may oppose registration on certain grounds. If there are no oppositions, or any oppositions are overcome, a certificate of registration will issue. The term of registration in Australia is 10 years