Theorems · Theorem · combinatorics
Matroid.IsCircuit.finite
∀ {α : Type u_1} {M : Matroid α} {C : Set α} [M.Finitary], M.IsCircuit C → C.Finite- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.Finitary
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepproof · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCircuit.depproof · cited by 15
- Matroid.Dep.not_indepproof · cited by 14
- Matroid.Finitarystatement and proof · cited by 11
- Matroid.IsCircuit.eq_of_not_indep_subsetproof · cited by 3
- Matroid.indep_iff_forall_finite_subset_indepproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.exists_mem_finite_closure_of_mem_closureproof · cited by 1
- Matroid.finitary_iff_forall_isCircuit_finiteproof · cited by 0