# Two new theorems

I’ve proved the theorem:

Theorem

1. $f \mapsto \bigsqcap^{\mathsf{RLD}} f$ and $\mathcal{A} \mapsto \Gamma (A ; B) \cap \mathcal{A}$ are mutually inverse bijections between $\mathfrak{F} (\Gamma (A ; B))$ and funcoidal reloids.
2. These bijections preserve composition.

(The second items is the previously unknown fact.)

and its consequence:

Theorem $(\mathsf{RLD})_{\Gamma} g \circ (\mathsf{RLD})_{\Gamma} f = (\mathsf{RLD})_{\Gamma} (g \circ f)$ for every composable funcoids $f$ and $g$.

See this online article for the proofs.