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Theorem 5.2. The “One Ring” theorem:
(∃x)((x∊Ring)∧(∀y)((y∊Ring)∧¬(y=x))⇒((|x|>y)∧(i(x,y)→i(y))∧(d(x,y)→0)∧(Light(y)→0)∧(dy/dt→0)
This theorem was proved constructively by Sauron in
1600; his elegant and powerful proof, acclaimed by mathematicians
of the time as “precious” and said to have played a
major part in attracting at least nine promising graduate
students to Barad-dur University, was unfortunately
lost at the end of the Second Age, and independently
rediscovered by Baggins in 2941. The details of the
proof will not be given here; the curious student is
advised to consult any standard text on ring theory.
Gandalf 3016 (Vol. III, pp. 4106-9) is particularly
recommended.