Theorems · Theorem · combinatorics
Matroid.Indep.isBasis_setOfPred_insert_isBasis
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → M.IsBasis I {x | M.IsBasis I (insert x I)}- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.ofPredstatement and proof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Set.insert_eq_of_memproof · cited by 118
- Matroid.IsBasis.subset_groundproof · cited by 31
- Matroid.Indep.isBasis_selfproof · cited by 12
- Matroid.Indep.isBasis_of_forall_insertproof · cited by 5
- Matroid.Indep.eq_of_isBasisproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.Indep.isBasis_closureproof · cited by 5
- Matroid.Indep.isBasis_setOf_insert_isBasisproof · cited by 0