Now that those formal transformations have been done, PostgreSQL will perform an exhaustive search. It will try out all the possible plans and come up with the cheapest solution to your query. PostgreSQL knows which indexes are possible and just uses the cost model to determine how to do things in the best way possible.

During an exhaustive search, PostgreSQL will also try to determine the best join order. In the original query, the join order was fixed to A → B and A → C. However, using those equality constraints, we could join B → C and join A later. All of these options are open to the planner.