Theorems · Theorem · combinatorics
Matroid.IsNonloop.of_restrict
∀ {α : Type u_1} {M : Matroid α} {e : α} {R : Set α}, (M.restrict R).IsNonloop e → M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.restrictstatement and proof · cited by 111
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.restrict_isNonloop_iffproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsRestriction.isRestriction_removeLoopsproof · cited by 1
- Matroid.IsNonloop.of_isRestrictionproof · cited by 0
- Matroid.isNonloop_iff_restrict_of_memproof · cited by 0