I’ve proved some new theorems. The proofs are currently available in this PDF file.

**Theorem** The set of funcoids is with separable core.

**Theorem** The set of funcoids is with co-separable core.

**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\} $.

**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\} $.

It seems (I have not yet checked) that the following conjecture follows from the last theorem:

**Conjecture** Composition of complete reloids is complete.

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