Theorems · Theorem · combinatorics
Matroid.eRk_union_closure_left_eq
∀ {α : Type u_1} (M : Matroid α) (X Y : Set α), M.eRk (M.closure X ∪ Y) = M.eRk (X ∪ Y)- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ENatstatement and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Matroid.closurestatement and proof · cited by 272
- Matroid.eRkstatement and proof · cited by 101
- Matroid.eRk_closure_eqproof · cited by 8
- Matroid.closure_union_closure_left_eqproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsBasis'.eRk_eq_eRk_unionproof · cited by 3
- Matroid.eRk_insert_closure_eqproof · cited by 0