Theorems · Theorem · combinatorics
Matroid.IsNonloop.exists_mem_isCocircuit
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsNonloop e → ∃ K, M.IsCocircuit K ∧ e ∈ K- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBaseproof · cited by 239
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.IsCocircuitstatement · cited by 32
- Matroid.fundCocircuitproof · cited by 9
- Matroid.mem_fundCocircuitproof · cited by 3
- Matroid.fundCocircuit_isCocircuitproof · cited by 2
- Matroid.IsNonloop.exists_mem_isBaseproof · cited by 1
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