Theorems · Theorem · combinatorics
Matroid.exists_isNonloop
∀ {α : Type u_1} (M : Matroid α) [M.RankPos], ∃ e, M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankPos
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBaseproof · cited by 239
- Matroid.IsNonloopstatement and proof · cited by 65
- Set.Nonempty.someproof · cited by 53
- Set.Nonempty.some_memproof · cited by 42
- Matroid.IsBase.indepproof · cited by 22
- Matroid.RankPosstatement and proof · cited by 22
- Matroid.exists_isBaseproof · cited by 15
- Matroid.Indep.isNonloop_of_memproof · cited by 5
- Matroid.IsBase.nonemptyproof · cited by 2
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