In “Funcoids and Reloids” online draft there was an erroneous lemma:

**Lemma** For every two sets $latex S$ and $latex T$ of binary relations and every set $latex A$

$latex \bigcap {\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} T \Rightarrow \bigcap {\nobreak}^{\mathfrak{F}} \{ \langle F \rangle A | F \in S \} = \bigcap{\nobreak}^{\mathfrak{F}} \{ \left\langle G \right\rangle A | G \in T \}$.

The above lemma is false. The below modified lemma is true:

**Lemma** For every two filter bases $latex S$ and $latex T$ of binary relations and every set $latex A$

$latex \bigcap {\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} T \Rightarrow \bigcap {\nobreak}^{\mathfrak{F}} \{ \langle F \rangle A | F \in S \} = \bigcap{\nobreak}^{\mathfrak{F}} \{ \left\langle G \right\rangle A | G \in T \}$.

After correcting the lemma I corrected also the proof of the theorem which relies on this lemma:

**Theorem** $latex (\mathsf{FCD}) (g \circ f) = ((\mathsf{FCD} g)) \circ ((\mathsf{FCD}) f)$ for every reloids $latex f$ and $latex g$.