Theorems · Theorem · combinatorics
Matroid.map_dual
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {M : Matroid α} {hf : Set.InjOn f M.E}, (M.map f hf)✶ = M✶.map f hf- Defined in
- Mathlib.Combinatorics.Matroid.Map
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.imageproof · cited by 5,609
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Set.InjOnstatement and proof · cited by 543
- Matroid.IsBaseproof · cited by 239
- Set.sdiff_subsetproof · cited by 156
- Matroid.dualstatement and proof · cited by 79
- Matroid.mapstatement and proof · cited by 32
- Matroid.dual_isBase_iffproof · cited by 9
- Matroid.ext_isBaseproof · cited by 7
- Set.InjOn.image_sdiff_subsetproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.map_freeOnproof · cited by 0