# Isomorfism between inductive and coinductive types (through double negation)

The paper "CPS Translating Inductive and Coinductive Types" mentions that there is an isomorphism between inductive (mu) and coinductive (nu) types, which they use for their translation. It states that:

$$\neg\mu Z.A(\neg Z)\ \cong\ \nu Z.\neg A(Z)$$

...but it gives no more details about it. Is this isomorphism correct? Is it constructive? Where could I find more information about it?

I've spent several hours trying to prove (any side of) it on Coq, using the standard impredicative encodings for those (e.g., see here), but failed.