Theorems · Theorem · combinatorics
Matroid.loopyOn_closure_eq
∀ {α : Type u_2} (E X : Set α), (Matroid.loopyOn E).closure X = E- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 88 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
- Matroid.closurestatement · cited by 272
- Set.empty_unionproof · cited by 52
- Matroid.loopyOnstatement · cited by 32
- Set.empty_interproof · cited by 30
- Set.sdiff_emptyproof · cited by 25
- Matroid.emptyOnproof · cited by 15
- Matroid.restrict_closure_eq'proof · cited by 9
- Matroid.emptyOn_closure_eqproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.closure_empty_eq_ground_iffproof · cited by 3
- Matroid.eq_loopyOn_iff_loops_eqproof · cited by 1
- Matroid.eq_loopyOn_iff_loopsproof · cited by 1
- Matroid.loopyOn_isLoop_iffproof · cited by 0
- Matroid.loopyOn_spanning_iffproof · cited by 0