Theorems · Theorem · combinatorics
Matroid.IsColoop.sdiff_not_spanning
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e → ¬M.Spanning (M.E \ {e})Alias of the forward direction of Matroid.isColoop_iff_sdiff_not_spanning.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement · cited by 550
- Matroid.Spanningstatement · cited by 63
- Matroid.IsColoopstatement · cited by 38
- Matroid.isColoop_iff_sdiff_not_spanningproof · cited by 3
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