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More lemmas for `filter` w.r.t. maps

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Merged Robbert Krebbers requested to merge robbert/map_filter into master Sep 11, 2019
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  • filter P m ##ₘ filter (λ v, ¬ P v) m
  • filter P m ∪ filter (λ v, ¬ P v) m = m
  • (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) → dom D (filter P m) ≡ X

For the last one, I have repurposed the name dom_map_filter, which was previously used for dom D (filter P m) ⊆ dom D m. I have renamed the old lemma into dom_map_filter_subseteq. This follows current naming conventions.

This MR received partial contributions from @dfrumin.

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Source branch: robbert/map_filter