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Theorems · Theorem · combinatorics

Matroid.IsBasis.dep_of_ssubset

∀ {α : Type u_1} {M : Matroid α} {I X Y : Set α}, M.IsBasis I X → I ⊂ Y → Y ⊆ X → M.Dep Y
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
1 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.IsBasis.insert_dep · cited by 3IsBasis.insert_depSet · cited by 53352SetMatroid · cited by 1258MatroidLT.lt.ne · cited by 872lt.neMatroid.E · cited by 550Matroid.EMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.Dep · cited by 76Matroid.DepMatroid.IsBasis.subset_ground · cited by 31IsBasis.subset_groundLT.lt.subset · cited by 20lt.subsetMatroid.not_indep_iff · cited by 11Matroid.not_indep_iffMatroid.IsBasis.eq_of_subset_indep · cited by 8IsBasis.eq_of_subset_indepIsBasis.dep_of_ssubsetCITED BYCITES

Cites11

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Cited by1

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