Is It Lawful to Heal on the Sabbath?

The House of Halal allowed for the kindling of fire on the Sabbath, but this was prohibited by Beit Shemaier. In Matthew 12 verse 11, he says, what man shall there be among you that has a sheep? And if it falls into a pit on the Sabbath,. will he not lay hold on it and lift it out? Now that actually happened. They would dig pits to kind of trap wolves and predators, and sometimes sheep would fall into these pits. So here, the way I read this, Jesus is basically saying, listen, the Sabbath is for man. The Sabbath is to bless mankind. Use the day to do well."