Theorems · Theorem · combinatorics
Matroid.IsColoop.notMem_isCircuit
∀ {α : Type u_1} {M : Matroid α} {e : α} {C : Set α}, M.IsColoop e → M.IsCircuit C → e ∉ C- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.IsCircuitstatement and proof · cited by 108
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.IsNonloop.not_isLoopproof · cited by 8
- Matroid.IsCircuit.isCocircuitproof · cited by 1
- Matroid.IsCocircuit.isNonloop_of_memproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.disjoint_coloopsproof · cited by 1
- Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuitproof · cited by 0
- Matroid.IsCircuit.not_isColoop_of_memproof · cited by 0