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Theorems · Theorem · combinatorics

Matroid.freeOn_isBasis_iff

∀ {α : Type u_1} {E I X : Set α}, (Matroid.freeOn E).IsBasis I X ↔ I = X ∧ X ⊆ E
Defined in
Mathlib.Combinatorics.Matroid.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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Matroid.freeOn_isBasis'_iff · cited by 1Matroid.freeOn_isBasis'_i…Set · cited by 53352SetMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.IsBasis.subset_ground · cited by 31IsBasis.subset_groundMatroid.freeOn · cited by 25Matroid.freeOnMatroid.Indep.isBasis_self · cited by 12Indep.isBasis_selfMatroid.Indep.eq_of_isBasis · cited by 4Indep.eq_of_isBasisMatroid.freeOn_indep · cited by 3Matroid.freeOn_indepMatroid.freeOn_isBasis_iffCITED BYCITES

Cites7

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Cited by1

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