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Theorems · Theorem · combinatorics

Matroid.closure_spanning_iff

∀ {α : Type u_2} {M : Matroid α} {S : Set α},
  autoParam (S ⊆ M.E) Matroid.closure_spanning_iff._auto_1 → (M.Spanning (M.closure S) ↔ M.Spanning S)
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.IsBase.compl_closure_sdiff_singleton_isCocircuit · cited by 1IsBase.compl_closure_sdif…Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.closure · cited by 272Matroid.closureMatroid.Spanning · cited by 63Matroid.SpanningMatroid.closure_subset_ground · cited by 23Matroid.closure_subset_gr…Matroid.closure_closure · cited by 14Matroid.closure_closureMatroid.spanning_iff_closure_eq · cited by 7Matroid.spanning_iff_clos…Matroid.closure_spanning_iffCITED BYCITES

Cites8

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Cited by1

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