Mathlib Map

Theorems · Theorem · combinatorics

Matroid.loops_eq_empty

∀ {α : Type u_1} (M : Matroid α) [M.Loopless], M.loops = ∅
Defined in
Mathlib.Combinatorics.Matroid.Loop
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
Matroid.Loopless
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.isNonloop_of_loopless · cited by 6Matroid.isNonloop_of_loop…Matroid.IsRestriction.loopless · cited by 0IsRestriction.looplessSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.loops · cited by 52Matroid.loopsMatroid.Loopless · cited by 16Matroid.LooplessMatroid.Loopless.loops_eq_empty · cited by 1Loopless.loops_eq_emptyMatroid.loops_eq_emptyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.