Theorems · Theorem · combinatorics
Matroid.IsRkFinite.indep_of_encard_le_eRk
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.IsRkFinite I → I.encard ≤ M.eRk I → M.Indep I- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENatstatement · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- LE.le.trans_ltproof · cited by 795
- LE.le.antisymmproof · cited by 507
- Matroid.Indepstatement · cited by 367
- Set.encardstatement and proof · cited by 327
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsRkFinitestatement and proof · cited by 53
- Matroid.eRk_le_encardproof · cited by 10
- Matroid.indep_iff_eRk_eq_encard_of_finiteproof · cited by 5
- Matroid.IsRkFinite.eRk_lt_topproof · cited by 3
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