Here is a more explicit statement of what the theorem asserts.
What the theorem is saying in substance is that......
This theorem accounts for the term “subharmonic”.
Theorem 2 will form the basis for our subsequent results. [Not: “The Theorem 2”]
In particular, the theorem applies to weakly confluent maps.
Finally, case (E) is completed by again invoking Theorem 1.
At this stage we appeal to Theorem 2 to deduce that......
Hörmander's theorem [without “the”] = the Hörmander theorem
a theorem of Hörmander's [= one of Hörmander's theorems]
......, which, by another theorem of Kimney's, is more than enough to guarantee that P gives A outer measure 1.