Theorems · Theorem · combinatorics
Matroid.restrict_loops_eq
∀ {α : Type u_1} {M : Matroid α} {R : Set α}, R ⊆ M.E → (M.restrict R).loops = M.loops ∩ R- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Estatement and proof · cited by 550
- Matroid.restrictstatement · cited by 111
- Set.union_emptyproof · cited by 78
- Matroid.loopsstatement and proof · cited by 52
- Set.sdiff_eq_emptyproof · cited by 24
- Matroid.restrict_loops_eq'proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsRestriction.looplessproof · cited by 0