Theorems · Theorem · combinatorics
Matroid.eRk_lt_encard_of_dep_of_finite
∀ {α : Type u_1} {M : Matroid α} {X : Set α}, X.Finite → M.Dep X → M.eRk X < X.encard- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.encardstatement and proof · cited by 327
- lt_of_le_of_neproof · cited by 230
- Matroid.eRkstatement and proof · cited by 101
- Matroid.Depstatement and proof · cited by 76
- Matroid.eRk_le_encardproof · cited by 10
- Matroid.Indep.not_depproof · cited by 7
- Matroid.indep_iff_eRk_eq_encard_of_finiteproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.eRk_lt_encard_iff_dep_of_finiteproof · cited by 0