Correction on the recent theorems

About new theorems in in this my blog post:

I’ve simplified this theorem:

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

into

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

For a proof see this note.

The next theorem:

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