Theorems · Theorem · combinatorics
Matroid.Indep.notMem_closure_sdiff_of_mem
∀ {α : Type u_2} {M : Matroid α} {e : α} {I : Set α}, M.Indep I → e ∈ I → e ∉ M.closure (I \ {e})- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.closurestatement · cited by 272
- Matroid.indep_iff_forall_notMem_closure_sdiff'proof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.Indep.indep_insert_sdiff_of_mem_closureproof · cited by 2
- Matroid.IsBase.isBase_insert_sdiff_of_mem_closureproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- Matroid.Indep.union_indep_iff_forall_notMem_closure_rightproof · cited by 1
- Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuitproof · cited by 0
- Matroid.Indep.notMem_closure_diff_of_memproof · cited by 0