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Theorems · Theorem · combinatorics

Matroid.freeOn_closure_eq

∀ {α : Type u_2} (E X : Set α), (Matroid.freeOn E).closure X = X ∩ E
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
2 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Matroid.uniqueBaseOn_closure_eq · cited by 1Matroid.uniqueBaseOn_clos…Matroid.freeOn_not_isLoop · cited by 0Matroid.freeOn_not_isLoopSet · cited by 53352SetMatroid · cited by 1258MatroidSet.inter_subset_right · cited by 329Set.inter_subset_rightMatroid.closure · cited by 272Matroid.closureMatroid.freeOn · cited by 25Matroid.freeOnMatroid.closure_inter_ground · cited by 22Matroid.closure_inter_gro…Matroid.Indep.mem_closure_iff' · cited by 5Indep.mem_closure_iff'Matroid.freeOn_indep · cited by 3Matroid.freeOn_indepMatroid.freeOn_closure_eqCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.