Theorems · Theorem · combinatorics
Matroid.IsBasis.isBasis_of_isBasis_of_subset_of_subset
∀ {α : Type u_1} {M : Matroid α} {I X Y J : Set α}, M.IsBasis I X → M.IsBasis J Y → J ⊆ X → I ⊆ Y → M.IsBasis I Y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- Matroid.IsBasisstatement and proof · cited by 219
- Set.subset_interproof · cited by 74
- Matroid.IsBasis.subsetproof · cited by 45
- Matroid.IsBasis.isBasis_subsetproof · cited by 12
- Matroid.IsBasis.transferproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6