Extend faithfully

By an extension theorem we mean a theorem which guarantees that, given subsets Y and Z of X, a faithful map x from Y of X extends faithfully to a map from Z of X. 

The goal of this section is the proof of Theorem 11.4.6. In this theorem, we focus on faithful maps from certain subsets Y of X to X which extend faithfully to a subset of X containing Y and one additional element. The main idea of the proof of this theorem is the use of Corollary 11.4.3 in the proof of Proposition 11.4.5. 

Corollary 11.4.8 Each faithful map from yV to X extends faithfully to a bijective map from yV U zV to yxY U zxV1. ... 

X extends faithfully to a map from yV U2V to X. Thus, by Lemma 12.2.6, there exists, for each element w in x L, a uniquely determined element Xw in which is IC-compatible with Xz-... 

---