Theorems · Theorem · combinatorics
Matroid.Indep.fundCircuit_isCircuit
∀ {α : Type u_1} {M : Matroid α} {I : Set α} {e : α},
M.Indep I → e ∈ M.closure I → e ∉ I → M.IsCircuit (M.fundCircuit e I)- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Set.sInterproof · cited by 225
- Set.sdiff_subsetproof · cited by 156
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.Indep.subsetproof · cited by 42
- Set.sInter_subset_of_memproof · cited by 28
- Matroid.fundCircuitstatement · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.Dep.exists_isCircuit_subsetproof · cited by 5
- Matroid.IsBase.fundCircuit_isCircuitproof · cited by 2
- Matroid.fundCocircuit_isCocircuitproof · cited by 2
- Matroid.exists_isCircuit_of_mem_closureproof · cited by 2
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0