Theorems · Theorem · combinatorics
Matroid.IsRestriction.isRestriction_removeLoops
∀ {α : Type u_1} {M N : Matroid α}, N.IsRestriction M → ∀ [N.Loopless], N.IsRestriction M.removeLoops- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.Loopless
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.restrictproof · cited by 111
- Matroid.IsRestrictionstatement and proof · cited by 45
- Matroid.removeLoopsstatement · cited by 17
- Matroid.Looplessstatement and proof · cited by 16
- Matroid.isNonloop_of_looplessproof · cited by 6
- Matroid.IsNonloop.of_restrictproof · cited by 3
- Matroid.IsRestriction.exists_eq_restrictproof · cited by 2
- Matroid.IsRestriction.of_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.removeLoops_mono_isRestrictionproof · cited by 0