I have just proven the following two new theorems:

**Theorem** Composition of complete reloids is complete.

**Theorem** $latex (\mathsf{RLD})_{\mathrm{out}} g \circ (\mathsf{RLD})_{\mathrm{out}} f = (\mathsf{RLD})_{\mathrm{out}} (g \circ f)$ if $latex f$ and $latex g$ are both complete funcoids (or both co-complete).

See this note for the proofs.