Theorems · Theorem · combinatorics
Matroid.closure_sdiff_loops_eq
∀ {α : Type u_1} (M : Matroid α) (X : Set α), M.closure (X \ M.loops) = M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Matroidstatement and proof · cited by 1,258
- Matroid.closurestatement and proof · cited by 272
- Set.union_emptyproof · cited by 78
- Matroid.loopsstatement and proof · cited by 52
- Set.sdiff_union_selfproof · cited by 30
- Matroid.closure_union_closure_right_eqproof · cited by 6
- Matroid.closure_emptyproof · cited by 5
- Matroid.closure_union_loops_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.closure_inter_setOfPred_isNonloop_eqproof · cited by 1
- Matroid.closure_diff_loops_eqproof · cited by 0