It is my first time reading this GTM$167$ and learning the Galois theory.
(1) I don't understand what's the meaning of 'inclusion reversing correspondence'. I guess it refers to the 1 and 3 in the Lemma 2.9. Is that right?
(2) In the second picture, 'a necessary condition from part $5$ is that $F$ is the fixed field of Gal($K/F$)'. Why is that?
