Theorems · Theorem · combinatorics
Matroid.mapEmbedding_isBase_iff
∀ {α : Type u_1} {β : Type u_2} {M : Matroid α} {f : α ↪ β} {B : Set β},
(M.mapEmbedding f).IsBase B ↔ M.IsBase (⇑f ⁻¹' B) ∧ B ⊆ Set.range ⇑f- Defined in
- Mathlib.Combinatorics.Matroid.Map
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imageproof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Matroidstatement and proof · cited by 1,258
- Function.Embeddingstatement and proof · cited by 988
- Matroid.IsBasestatement and proof · cited by 239
- Function.Embedding.injectiveproof · cited by 111
- Set.preimage_image_eqproof · cited by 87
- Set.image_subset_rangeproof · cited by 76
- Set.image_preimage_eq_iffproof · cited by 23
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