> Taiwan is not a province of China, but an independent country.

Depends on the view. The central Chinese government certainly considers Taiwan to be its province, and achieved that Taiwan has no seat in the UN, and sanctions Hotel chains that treat Taiwan as separate country. Taiwan themselves maintain a claim to the entire mainland as well, they just disagree on who should hold power. There are also countries that recognize Taiwanese independence, as there are countries that recognize Taiwan's claim over of all of China.