This method is used, for example, in the proof that there is no free complete lattice.

We shall use this notation also in the proof.

Again, we must resort to the assumptions whose strength we specifically "tuned" for using in the proof.

The following general results are used in the proof.

It is used in the proof of Gödel's completeness theorem, among other places.

This is one of the steps used in the proof of the Weil conjectures.

For example, it is used in the proof that every compact 3-manifold has a standard spine.

The latter formulation has been used in the proof the conjecture.

There is also an easy to read, freely available on-line, research announcement article, but it only hints at the ideas used in the proof.

The global method was used in the proof of Ushiki's Theorem.