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November 30, 2014 / porton

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.

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