New easy theorem and a couple of conjectures

I added to my free ebook a new (easy to prove) theorem and a couple new conjectures:

Theorem For every reloid $latex f$:

1. $latex \mathsf{Compl} (\mathsf{FCD}) f = (\mathsf{FCD}) \mathsf{Compl} f$;
2. $latex \mathsf{CoCompl} (\mathsf{FCD}) f = (\mathsf{FCD}) \mathsf{CoCompl} f$.

Conjecture

1. $latex \mathsf{Compl}(\mathsf{RLD})_{\mathsf{in}} g=(\mathsf{RLD})_{\mathsf{in}}\mathsf{Compl} g$;
2. $latex \mathsf{Compl}(\mathsf{RLD})_{\mathsf{out}} g=(\mathsf{RLD})_{\mathsf{out}}\mathsf{Compl} g$;.