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Theorems · Theorem · combinatorics

Matroid.loopyOn_isBasis_iff

∀ {α : Type u_1} {E I X : Set α}, (Matroid.loopyOn E).IsBasis I X ↔ I = ∅ ∧ X ⊆ E
Defined in
Mathlib.Combinatorics.Matroid.Constructions
Cited by
0 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.IsBasis.indep · cited by 51IsBasis.indepMatroid.loopyOn · cited by 32Matroid.loopyOnMatroid.IsBasis.subset_ground · cited by 31IsBasis.subset_groundMatroid.isBasis_iff · cited by 4Matroid.isBasis_iffMatroid.loopyOn_indep_iff · cited by 2Matroid.loopyOn_indep_iffMatroid.loopyOn_isBasis_iffCITED BYCITES

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