Theorems · Theorem · combinatorics
Matroid.ext_isBase
∀ {α : Type u_1} {M₁ M₂ : Matroid α}, M₁.E = M₂.E → (∀ ⦃B : Set α⦄, B ⊆ M₁.E → (M₁.IsBase B ↔ M₂.IsBase B)) → M₁ = M₂- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, 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
- Set.extproof · cited by 2,266
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- LE.le.trans_eqproof · cited by 328
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.extproof · cited by 2
- Matroid.indep_iff'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.dual_dualproof · cited by 22
- Matroid.ext_indepproof · cited by 15
- Matroid.finite_setOfPred_matroidproof · cited by 2
- Matroid.comapOn_dual_eq_of_bijOnproof · cited by 1
- Matroid.map_dualproof · cited by 1
- Matroid.uniqueBaseOn_dual_eqproof · cited by 1
- Matroid.ext_iff_isBaseproof · cited by 0