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See the very nice paper by Eisenbud, Green, and Harris: @article {MR1376653, AUTHOR = {Eisenbud, David and Green, Mark and Harris, Joe}, TITLE = {Cayley-{B}acharach theorems and conjectures}, …

Why mean sojourn time theorem is not the pointwise ergodic theorem with $f=\chi_U?$ And mean sojourn time theorem iff ergodicity. … And of course there are many proves of mean sojourn time theorem that do not use pointwise ergodic theorem. …

In dimension 3, you have the sphere theorem, the torus theorem, the annulus theorem, and the disk theorem (which is the loop theorem and Dehn's lemma put together). … So, if you didn't require the sphere to be embedded, and the problem already had an affirmative answer, I'd call it the Ball Theorem. …

(Mac Lane's Theorem) Prove that every diagram commutes. 5. … Using theorems from both Freyd and Mitchell, prove that every reflective category is co-reflective. Dualize. 11. …

There are many possible approaches to the loop and sphere theorems now available. … One may also deduce the loop theorem from the sphere theorem by doubling. These theorems also follow as corollaries of the geometrization theorem. …

So I suppose the following would be examples of answers to the question: Ramsey's theorem; van der Waerden's theorem; the Hales-Jewett theorem; Szemeredi's theorem; the Green-Tao theorem. … Especially infinite versions of such theorems seem to match nicely with your example of the central limit theorem. …

You say "Especially in the context of theorem provers: ..." then go on to describe conflating content and presentation. The content is a dependency tree of theorems. … Until theorem provers start proving theorems about the difficulty in understanding a statement and proof assuming a reader model, this is not in the context of theorem provers.) …

More generally, this argument shows something like this: if there exist two theorems which are “essentially different”, then there exists a theorem with two proofs which are “essentially different”. … Or, contapositively, if all proofs of any given theorem are “essentially the same”, then in fact all theorems are “essentially the same”. …

Edmund Landau had theorems only, and otherwise nothing (when it comes to naming special statements which required a proof; there should be also definitions and axioms on the top of the theorems). … Section 2.4 The fundamental Theorem of Algebra (while, inside the section, this theorem could be Theorem 72, with a sentence of an explanation preceding that theorem). …

There's a combination theorem of Bestvina-Feighn for hyperbolic groups. … There are gluing theorems for $CAT(\kappa)$ spaces in Chapter 11 of Bridson-Haefliger which can give rise to combination theorems for groups. …

Since this question was written, there is a paper 2-dimensional bifunctor theorems and distributive laws by Faul–Manuell–Siqueira based on this idea. … In particular, they prove a "bifunctor theorem" for lax functors between 2-categories (Theorem 3.2), and relate it to certain tensor products of 2-categories (see Theorem 4.10, the end of §4, and Theorem …

Philip F Reichmeider, The Equivalence of Some Combinatorial Matching Theorems. … A fine little book about Hall's Marriage Theorem, Konig's Theorem, Dilworth's Theorem, Ford-Fulkerson, and so on, and the relations among them. …

Theorem 1 does not require computer assistance, while Theorem 2 and Theorem 3 both do require computer assistance. … Thus, given that it took a computer 9 times longer to verify Theorem 2 than Theorem 3, and Theorem 3 apparently can be verified by hand in a few months (let us define few=3), then under some very dubious …

If the hypothesis of a theorem is a disjunction, you can always split the theorem up into two theorems with separate hypotheses, and doing so will often clarify the statement and proof anyway. … (Dually, if the conclusion of a theorem is a conjunction, then you can split it up into two theorems with separate conclusions. …

I would state the main result up front, along the lines of: In this paper we prove the following theorem: Theorem A: (statement of theorem A) Then go on with the explanation of the proof, including … Then you can finish with: Theorem A follows simply as a corollary. …