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Theorems · Theorem · combinatorics

Matroid.IsBase.isBasis_ground

∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → M.IsBasis B M.E
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
4 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.cardinalMk_eq · cited by 2IsBase.cardinalMk_eqMatroid.Coindep.delete_isBase_iff · cited by 2Coindep.delete_isBase_iffMatroid.IsBase.cardinalMk_sdiff_comm · cited by 1IsBase.cardinalMk_sdiff_c…Matroid.IsBase.eRk_eq_eRank · cited by 0IsBase.eRk_eq_eRankSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.isBasis_ground_iff · cited by 10Matroid.isBasis_ground_iffIsBase.isBasis_groundCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.