Theorems · Theorem · combinatorics
Matroid.IsBasis.contract_sdiff_isBasis_sdiff
∀ {α : Type u_1} {M : Matroid α} {I J X Y : Set α},
M.IsBasis I X → M.IsBasis J Y → I ⊆ J → (M.contract I).IsBasis (J \ I) (Y \ X)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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
- LE.le.transproof · cited by 3,151
- Disjointproof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Set.inter_subset_rightproof · cited by 329
- Matroid.IsBasisstatement and proof · cited by 219
- Set.sdiff_subsetproof · cited by 156
- Matroid.contractstatement · cited by 103
- Set.subset_interproof · cited by 74
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.IsBasis.subsetproof · cited by 45
- Set.subset_sdiffproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.contract_diff_isBasis_diffproof · cited by 0