refactor(set_theory/game/*): fix theorem names (#14685)
Some theorems about `exists` had `forall` in the name, other theorems about swapped `≤` or `⧏` used `le` and `lf` instead of `ge` and `gf`.
We also golf `le_of_forall_lt`.
Co-authored-by: Junyan Xu <junyanxumath@gmail.com>
