Theorems · Theorem · combinatorics
Matroid.eRk_lt_encard_iff_dep_of_finite
∀ {α : Type u_1} {M : Matroid α} {X : Set α},
X.Finite → autoParam (X ⊆ M.E) Matroid.eRk_lt_encard_iff_dep_of_finite._auto_1 → (M.eRk X < X.encard ↔ M.Dep X)- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 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
- Set.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- LT.lt.neproof · cited by 872
- Matroid.Estatement and proof · cited by 550
- Set.encardstatement and proof · cited by 327
- Matroid.eRkstatement and proof · cited by 101
- Matroid.Depstatement and proof · cited by 76
- Matroid.not_indep_iffproof · cited by 11
- Matroid.indep_iff_eRk_eq_encard_of_finiteproof · cited by 5
- Matroid.eRk_lt_encard_of_dep_of_finiteproof · cited by 1
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