Theorems · Theorem · combinatorics
Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuit
∀ {α : Type u_1} {M : Matroid α} {e : α} {B : Set α},
M.IsBase B → e ∈ B → (M.IsColoop e ↔ ∀ x ∈ M.E \ B, e ∉ M.fundCircuit x B)- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
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
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBasestatement and proof · cited by 239
- Set.sdiff_subsetproof · cited by 156
- emproof · cited by 115
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.closure_subset_closureproof · cited by 24
- Matroid.subset_closureproof · cited by 23
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