Theorems · Theorem · combinatorics
Matroid.eq_loopyOn_iff_loops
∀ {α : Type u_1} {M : Matroid α} {E : Set α}, M = Matroid.loopyOn E ↔ M.loops = E ∧ M.E = E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.loopsstatement and proof · cited by 52
- Matroid.loopyOnstatement and proof · cited by 32
- Matroid.loopyOn_closure_eqproof · cited by 5
- Matroid.closure_empty_eq_ground_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.restrict_subset_loops_eqproof · cited by 0