Theorems · Theorem · combinatorics
Matroid.mem_ground_of_mem_closure
∀ {α : Type u_2} {M : Matroid α} {X : Set α} {e : α}, e ∈ M.closure X → e ∈ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 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.Estatement · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Matroid.closure_subset_groundproof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.fundCircuit_eq_sInterproof · cited by 3
- Matroid.Indep.indep_insert_sdiff_of_mem_closureproof · cited by 2
- Matroid.Indep.insert_isCircuit_of_forallproof · cited by 2
- Matroid.Indep.mem_fundCircuit_iffproof · cited by 1
- Matroid.contract_closure_eqproof · cited by 1