As basic hygiene, please state theorems ***before, not after*** their proofs. I find nothing more annoying than the style where some seemingly random agitation is followed by

> ... and therefore we have proved:
>
> **Theorem 3.47** Let a regular gizmo have transversality property (3.25). Then the closed sub-gizmo (3.20) has property (3.30).

The problem with such a structure is that it may in fact be impossible to rewrite in the normal theorem-proof order, because *only after half the proof* does "(3.20)" turn out to be well-defined, let alone closed; or properties "(3.25)" and "(3.30)" may be impossible to even state outside the context of the proof, e.g. because they involve auxiliary objects whose existence was not assured a priori.

So instead, 1º) set up the minimal environment where the result may be meaningfully stated; then 2º) state and 3º) prove it. Or at least, make sure that this *could be done*.