Theorems · Theorem · combinatorics
Matroid.Indep.eq_of_isBasis
∀ {α : Type u_1} {M : Matroid α} {I J : Set α}, M.Indep I → M.IsBasis J I → J = I- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Eq.subsetproof · cited by 124
- Matroid.IsBasis.subsetproof · cited by 45
- Matroid.IsBasis.eq_of_subset_indepproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.Indep.isBasis_setOfPred_insert_isBasisproof · cited by 3
- Matroid.freeOn_isBasis_iffproof · cited by 1
- Matroid.eRk_freeOnproof · cited by 0