Mathlib Map

Theorems · Theorem · combinatorics

Matroid.exists_mem_isCircuit_of_not_isColoop

∀ {α : Type u_1} {M : Matroid α} {e : α}, e ∈ M.E → ¬M.IsColoop e → ∃ C, M.IsCircuit C ∧ e ∈ C
Defined in
Mathlib.Combinatorics.Matroid.Loop
Cited by
0 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.IsCircuit · cited by 108Matroid.IsCircuitMatroid.IsColoop · cited by 38Matroid.IsColoopMatroid.fundCircuit · cited by 19Matroid.fundCircuitMatroid.IsBase.fundCircuit_isCircuit · cited by 2IsBase.fundCircuit_isCirc…Matroid.exists_mem_isCircuit_…CITED BYCITES

Cites8

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.