pufferffish / agda-symmetries

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Prove section to homomorphism to SList implies linear order #74

Closed pufferffish closed 8 months ago

pufferffish commented 9 months ago

TODOs:

  1. Formalize the proof that every set is well ordered implies AC implies contradiction with univalence (Theorem 3.2.2 from HoTT book, Diaconescu's theorem)
  2. Assume A is a linear order, show q : List A -> SList A this has a section, define is-sorted and sorted using fibre and image, show that tail of sorted list is a sorted list
  3. Prove converse of 2