Mathlib Map

Theorems · Theorem · combinatorics

Matroid.cRk_insert_closure_eq

∀ {α : Type u} (M : Matroid α) [M.InvariantCardinalRank] (e : α) (X : Set α),
  M.cRk (insert e (M.closure X)) = M.cRk (insert e X)
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
0 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Matroid.InvariantCardinalRank
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set · cited by 53352SetCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidMatroid.closure · cited by 272Matroid.closureSet.union_singleton · cited by 107Set.union_singletonMatroid.cRk · cited by 29Matroid.cRkMatroid.InvariantCardinalRank · cited by 25Matroid.InvariantCardinal…Matroid.cRk_union_closure_left_eq · cited by 2Matroid.cRk_union_closure…Matroid.cRk_insert_closure_eqCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.