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Theorems · Theorem · combinatorics

Matroid.spanning_iff_compl_coindep

∀ {α : Type u_2} {M : Matroid α} {S : Set α},
  autoParam (S ⊆ M.E) Matroid.spanning_iff_compl_coindep._auto_1 → (M.Spanning S ↔ M.Coindep (M.E \ S))
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
2 results in Mathlib
Foundations
Depth 92 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.isColoop_tfae · cited by 4Matroid.isColoop_tfaeMatroid.Spanning.compl_coindep · cited by 0Spanning.compl_coindepSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.Spanning · cited by 63Matroid.SpanningMatroid.Coindep · cited by 24Matroid.CoindepSet.sdiff_sdiff_cancel_left · cited by 21Set.sdiff_sdiff_cancel_le…Matroid.coindep_iff_compl_spanning · cited by 5Matroid.coindep_iff_compl…Matroid.spanning_iff_compl_co…CITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.