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

What are the intuitions or motivations for subcountability?

What references prove that subcountability is consistent with CZF?