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Theorems · Theorem · combinatorics

Matroid.empty_isBase_iff

∀ {α : Type u_1} {M : Matroid α}, M.IsBase ∅ ↔ M = Matroid.loopyOn M.E
Defined in
Mathlib.Combinatorics.Matroid.Constructions
Cited by
2 results in Mathlib
Foundations
Depth 82 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.eq_loopyOn_or_rankPos · cited by 0Matroid.eq_loopyOn_or_ran…Matroid.not_rankPos_iff · cited by 0Matroid.not_rankPos_iffSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.Indep.subset_ground · cited by 61Indep.subset_groundMatroid.loopyOn · cited by 32Matroid.loopyOnMatroid.empty_isBase_iffCITED BYCITES

Cites7

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Cited by2

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