Temporal Type Theory by Patrick Schultz & David I. Spivak

Author:Patrick Schultz & David I. Spivak
Language: eng
Format: epub
ISBN: 9783030007041
Publisher: Springer International Publishing

Proof

The first claim is easy: is d < t < u ⇒ (t < r′∨ r < t), which is obvious. For the second claim, Lemma 5.21 says that is equivalent to (d < t < u ⇒ t < r′) ∨ (d < t < u ⇒ r < t). Assume the first case; since either d < r′ or r′≤ d, we may assume d < r′ in which case we apply Lemma 5.22(e). The second case is similar.

For the third claim, the left-hand side is equivalent to and the right-hand side is equivalent to . The result follows from the second claim and Lemma 5.21. □

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