Theorems · Theorem · combinatorics
Matroid.restrictSubtype_isBasis_iff
∀ {α : Type u_1} {M : Matroid α} {Y : Set α} {I X : Set ↑Y},
(M.restrictSubtype Y).IsBasis I X ↔ M.IsBasis' (Subtype.val '' I) (Subtype.val '' X)- Defined in
- Mathlib.Combinatorics.Matroid.Map
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Function.Injective.injOnproof · cited by 280
- Subtype.val_injectiveproof · cited by 232
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.restrictproof · cited by 111
- Matroid.IsBasis'statement and proof · cited by 101
- Subtype.coe_preimage_selfproof · cited by 46
- Matroid.IsBasis.subsetproof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.restrictSubtype_ground_isBasis_iffproof · cited by 0