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Fill in remaining axioms #2

Description

@SquidDev

There's a fair few lemmas and definitions within the codebase which are axiomised, and would be good to fill in:

Species

  • Some decision procedure for species equivalence.
  • Prime decomposition of species. Here we mostly need to be able to show things like is_prime nil.

Transitions

  • transition.rename_from - Effectively undoes a transition - if we have (rename A) —[a]→ E, then there is some a', E' such that rename a' = a, and likewise for E'.
  • Show that transition.equivalent_of is a bijection.
  • Provide some way of enumerating over every transition. Ideally as a fintype, but as a multiset/finset otherwise.
  • Decision procedure for transition equality.

Semantics

  • Show appropriate equalities for dP/dt and ∂P under ≡⁺.
  • Show process spaces are embedded in processes.

Non-cπ related

  • fin_fn.bind_distrib (fin_fn.bind distributes over +)
  • fin_fn.bind₂_swap (fin_fn.bind₂ can be swapped).

Activity

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