Commit 2025-03-31 13:41 82533ad0

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feat(Matroid/Rank): ENat-valued matroid rank (#23377) We define the ENat-valued rank M.eRank of a matroid M, and also the function M.eRk which gives the rank of each set in M. We give basic API for these functions, including submodularity. These are analogous to the existing cardinal-valued Matroid.cRank and Matroid.cRk, but are much nicer, because the bases of a matroid are always equicardinal in the sense of ENat-valued cardinality but not Cardinal-valued.

Estimated changes

added theorem Matroid.eRank_def
added theorem Matroid.eRank_emptyOn
added theorem Matroid.eRank_eq_top
added theorem Matroid.eRank_loopyOn
added theorem Matroid.eRank_map
added theorem Matroid.eRank_restrict
added theorem Matroid.eRk_closure_eq
added theorem Matroid.eRk_comap_eq
added theorem Matroid.eRk_empty
added theorem Matroid.eRk_eq_eRank
added theorem Matroid.eRk_ground
added theorem Matroid.eRk_le_eRank
added theorem Matroid.eRk_le_encard
added theorem Matroid.eRk_le_iff
added theorem Matroid.eRk_map_eq
added theorem Matroid.eRk_mono
added theorem Matroid.eRk_univ_eq
added theorem Matroid.eq_eRk_iff
added theorem Matroid.le_eRk_iff
added theorem Matroid.one_le_eRank