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Theorems · Theorem · combinatorics

Matroid.map_image_isBase_iff

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E} {B : Set α},
  B ⊆ M.E → ((M.map f hf).IsBase (f '' B) ↔ M.IsBase B)
Defined in
Mathlib.Combinatorics.Matroid.Map
Cited by
1 results in Mathlib
Foundations
Depth 97 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.map_dual · cited by 1Matroid.map_dualSet · cited by 53352SetSet.image · cited by 5609Set.imageMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.ESet.InjOn · cited by 543Set.InjOnMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.map · cited by 32Matroid.mapMatroid.IsBase.subset_ground · cited by 30IsBase.subset_groundSet.InjOn.image_eq_image_iff · cited by 8InjOn.image_eq_image_iffMatroid.map_isBase_iff · cited by 5Matroid.map_isBase_iffMatroid.map_image_isBase_iffCITED BYCITES

Cites10

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Cited by1

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