### Correction on the recent theorems

About new theorems in in this my blog post:

I’ve simplified this theorem:

Theorem A reloid $latex f$ is complete iff
$latex f = \bigsqcap^{\mathsf{RLD}} \left\{ \bigcup_{x \in \mathrm{Src}\, f} (\{ x \} \times \langle T \rangle^{\ast} \{ x \}) \, | \, T \in (\mathscr{P} \mathrm{Dst}\, f)^{\mathrm{Src}\, f}, \forall x \in A : \langle T \rangle^{\ast} \{ x \} \in G (x) \right\}$.

into

Theorem A reloid $latex f$ is complete iff $latex f=(\mathsf{RLD})_{\mathrm{out}} g$ for a complete funcoid $latex g$.

For a proof see this note.

The next theorem:

Theorem A funcoid $latex f$ is complete iff
$latex f = \bigsqcap^{\mathsf{FCD}} \left\{ \bigcup_{x \in \mathrm{Src}\, f} (\{ x \} \times \langle T \rangle^{\ast} \{ x \}) \, | \, T \in (\mathscr{P} \mathrm{Dst}\, f)^{\mathrm{Src}\, f}, \forall x \in A : \langle T \rangle^{\ast} \{ x \} \in G (x) \right\}$.

collapses into

Theorem $latex f=\bigsqcap^{\mathsf{FCD}} \mathrm{up}\, f$, what I proved long time ago.

So, I have removed this theorem from my writings.

Conjecture A funcoid $latex f$ is complete iff $latex f=(\mathsf{FCD}) g$ for a complete reloid $latex g$.