Theorems · Theorem · combinatorics
Matroid.IsBase.indep
∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → M.Indep B- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- subset_rflproof · cited by 77
- Matroid.indep_iffproof · cited by 4
Cited by22
Results whose statement or proof uses this declaration.
- Matroid.empty_indepproof · cited by 8
- Matroid.isBase_iff_maximal_indepproof · cited by 5
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.isLoop_tfaeproof · cited by 3
- Matroid.union_indep_iff_indep_of_subset_coloopsproof · cited by 3
- Matroid.IsBase.fundCircuit_isCircuitproof · cited by 2
- Matroid.fundCocircuit_isCocircuitproof · cited by 2
- Matroid.Spanning.isBase_restrict_iffproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- Matroid.ground_indep_iff_isBaseproof · cited by 1
- Matroid.IsColoop.isNonloopproof · cited by 1