Theorems · Theorem · combinatorics
Matroid.Indep.subset
∀ {α : Type u_1} {M : Matroid α} {I J : Set α}, M.Indep J → I ⊆ J → M.Indep I- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 42 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.
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
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.indep_iffproof · cited by 4
Cited by42
Results whose statement or proof uses this declaration.
- Matroid.empty_indepproof · cited by 8
- Matroid.Dep.supersetproof · cited by 6
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.Indep.fundCircuit_isCircuitproof · cited by 5
- Matroid.Indep.sdiffproof · cited by 4
- Matroid.Indep.closure_inter_eq_self_of_subsetproof · cited by 4
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.isLoop_tfaeproof · cited by 3
- Matroid.union_indep_iff_indep_of_subset_coloopsproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.IsBasis'.contract_isBasis'_sdiff_sdiff_of_subsetproof · cited by 3
- Matroid.isCircuit_iff_dep_forall_sdiff_singleton_indepproof · cited by 3