In these slides of a talk Giovanni Curi shows that the generalized uniformity principle follows from Troesltras uniformity principle and subcountability, which are both claimed to be consistent with CZF. Subcountabilities consistency with CZF is not surprising at all in light of counterintuitive results like subsets of finite sets aren’t necessarily finite, etc. But it does seem to have a different flavor.

Can you provide any intuitions/motivations for subcountability?

Can you provide any good references that proves subcountability is consistent with CZF?