Lemma

Belisarius 'Lemma: "If we bypass LEO stations, we can land men on the Moon by 1969, and return them safely to Earth."

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One of the results, published jointly with Abraham Wald, was on the Neyman-Pearson Lemma.

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To see an intuitive picture of why the Lemma on Successors gives us what we want, we may temporarily regard Precedes+ as the relation ‰¤.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Π will inherit from L the structure of a complete lattice, which will then automatically be orthomodular by Lemma 4.3.

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Now to prove the Lemma on Successors by induction, we need to reconfigure this Lemma to a form which can be used as the consequent of the Principle of Induction; i.e., we need something of the form

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Boston was down with all the elements of Hip Hop culture since the late 70's God bless Lecco's Lemma and Skippy White's.

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Given this proof of the Lemma on Successors, Theorem 5 is not far away.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

The best known example is that "The axiom of choice is obviously true, Zermelo's Theorem is obviously false, and who can tell about Zorn's Lemma," even though the three statements are logically equivalent.

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Now we can prove that Predecessor is a one-to-one relation from this Lemma and Hume's Principle (cf. Gg I, §108):

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

Lemma (ii) is nice but is easily subsumed my lemma (i).

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