Proposition 1: For sufficiently large N, the following six quantities can be made arbitrarily small:
a)
b)
c)
d)
e)
f)
Proof: The proof, which is something of a technical distraction, is deferred to the end of this section.
Theorem: [Insert great theorem here.]
Proof: [Clear intuitive proof, invoking Proposition 1.]
It remains to prove Proposition 1.
Proof of Proposition 1: [Insert long boring computations here.]
Or alternatively:
Theorem: [State theorem]
Proof: I claim that for sufficiently large N, the following six quantities can be made arbitrarily small: a),b),c),d),e),f).
Granting this claim, the proof proceeds as follows: [intuitive argument here].
It remains to prove the claim:
Proof of claim a):
Proof of claim b):
Etc.