Theorems · Theorem · combinatorics
Matroid.fundCircuit_eq_of_notMem_ground
∀ {α : Type u_1} {M : Matroid α} {X : Set α} {e : α}, e ∉ M.E → M.fundCircuit e X = {e}- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 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.
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.ofPredproof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.closureproof · cited by 272
- Set.sInterproof · cited by 225
- Eq.subsetproof · cited by 124
- Set.empty_subsetproof · cited by 70
- Matroid.closure_inter_groundproof · cited by 22
- Matroid.fundCircuitstatement · cited by 19
- Set.singleton_inter_eq_emptyproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.fundCocircuit_eq_of_notMem_groundproof · cited by 1
- Matroid.IsBase.mem_fundCocircuit_iff_mem_fundCircuitproof · cited by 0