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Theorems · Theorem · combinatorics

Matroid.IsBase.ssubset_ground

∀ {α : Type u_1} {M : Matroid α} {B : Set α} [h : M✶.RankPos], M.IsBase B → B ⊂ M.E
Defined in
Mathlib.Combinatorics.Matroid.Dual
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Matroid.RankPos
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Around this declaration

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

Matroid.Indep.ssubset_ground · cited by 0Indep.ssubset_groundSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.dual · cited by 79Matroid.dualMatroid.IsBase.subset_ground · cited by 30IsBase.subset_groundMatroid.RankPos · cited by 22Matroid.RankPosLE.le.ssubset_of_ne · cited by 16le.ssubset_of_neMatroid.ground_not_isBase · cited by 1Matroid.ground_not_isBaseIsBase.ssubset_groundCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.