Theorems · Theorem · combinatorics
Matroid.Coindep.delete_isBase_iff
∀ {α : Type u_1} {M : Matroid α} {B D : Set α}, M.Coindep D → ((M.delete D).IsBase B ↔ M.IsBase B ∧ Disjoint B D)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Disjointstatement and proof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.IsBasisproof · cited by 219
- Set.sdiff_subsetproof · cited by 156
- Matroid.deletestatement · cited by 86
- Matroid.IsBasis.subsetproof · cited by 45
- Matroid.IsBase.subset_groundproof · cited by 30
- Set.subset_sdiffproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.Coindep.delete_rankPosproof · cited by 0
- Matroid.Coindep.delete_spanning_iffproof · cited by 0