Theorems · Theorem · combinatorics
Matroid.fundCircuit_eq_sInter
∀ {α : Type u_1} {M : Matroid α} {I : Set α} {e : α},
e ∈ M.closure I → M.fundCircuit e I = insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.closure J})- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Eproof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Set.sInterstatement and proof · cited by 225
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- Set.sInter_subset_of_memproof · cited by 28
- Matroid.fundCircuitstatement · cited by 19
- Matroid.mem_ground_of_mem_closureproof · cited by 5
- Matroid.closure_subset_closure_iff_subset_closureproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.Indep.fundCircuit_isCircuitproof · cited by 5
- Matroid.Indep.mem_fundCircuit_iffproof · cited by 1
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0