Theorems · Theorem · combinatorics
Matroid.Indep.augment_finset
∀ {α : Type u_1} {M : Matroid α} {I J : Finset α},
M.Indep ↑I → M.Indep ↑J → I.card < J.card → ∃ e ∈ J, e ∉ I ∧ M.Indep (insert e ↑I)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.cardstatement and proof · cited by 2,327
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Finset.toFinset_coeproof · cited by 16
- Set.encard_eq_coe_toFinset_cardproof · cited by 3
- Matroid.Indep.augmentproof · cited by 2
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