Theorems · Definition · combinatorics
Matroid.loops
{α : Type u_1} → Matroid α → Set αMatroid.loops M is the closure of the empty set.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.closureproof · cited by 272
Cited by56
Results whose statement or proof uses this declaration.
- Matroid.IsLoopproof · cited by 55
- Matroid.coloopsproof · cited by 34
- Matroid.isLoop_iffstatement · cited by 6
- Matroid.closure_emptystatement · cited by 5
- Matroid.contract_loops_eqstatement · cited by 4
- Matroid.IsLoop.closurestatement · cited by 2
- Matroid.dual_coloopsstatement and proof · cited by 2
- Matroid.restrict_loops_eq'statement and proof · cited by 2
- Matroid.setOfPred_isNonloop_eqstatement · cited by 2
- Matroid.closure_eq_loops_of_subsetstatement and proof · cited by 2
- Matroid.isNonloop_iff_mem_compl_loopsstatement and proof · cited by 2
- Matroid.closure_sdiff_loops_eqstatement and proof · cited by 2