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Theorems · Theorem · combinatorics

Matroid.spanning_iff_ground_subset_closure

∀ {α : Type u_2} {M : Matroid α} {S : Set α},
  autoParam (S ⊆ M.E) Matroid.spanning_iff_ground_subset_closure._auto_1 → (M.Spanning S ↔ M.E ⊆ M.closure S)
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
1 results in Mathlib
Foundations
Depth 62 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.IsCircuit.inter_isCocircuit_ne_singleton · cited by 2IsCircuit.inter_isCocircu…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…subset_antisymm_iff · cited by 17subset_antisymm_iffMatroid.spanning_iff_closure_eq · cited by 7Matroid.spanning_iff_clos…Matroid.spanning_iff_ground_s…CITED BYCITES

Cites8

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Cited by1

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