Theorems · Theorem · combinatorics
Matroid.IsBasis.sdiff_subset_loops_contract
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis I X → X \ I ⊆ (M.contract I).loops- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.contractstatement · cited by 103
- Matroid.loopsstatement · cited by 52
- Set.union_sdiff_selfproof · cited by 28
- Matroid.subset_closureproof · cited by 23
- Matroid.IsBasis.subset_closureproof · cited by 15
- Set.sdiff_subset_iffproof · cited by 15
- Set.union_eq_self_of_subset_leftproof · cited by 13
- Matroid.contract_loops_eqproof · cited by 4
- Matroid.IsBasis.left_subset_groundproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.diff_subset_loops_contractproof · cited by 0