Theorems · Theorem · combinatorics
Matroid.fundCircuit_eq_of_mem
∀ {α : Type u_1} {M : Matroid α} {X : Set α} {e : α}, e ∈ X → M.fundCircuit e X = {e}The fundamental isCircuit of e and X has the junk value {e} if e ∈ X
- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.ofPredproof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.closureproof · cited by 272
- Set.Subset.rflproof · cited by 255
- Set.sInterproof · cited by 225
- Set.singleton_subset_iffproof · cited by 206
- Matroid.fundCircuitstatement · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.fundCocircuit_eq_of_notMemproof · cited by 0
- Matroid.IsBase.mem_fundCocircuit_iff_mem_fundCircuitproof · cited by 0