Theorems · Theorem · combinatorics
Matroid.fundCocircuit_isCocircuit
∀ {α : Type u_1} {M : Matroid α} {e : α} {B : Set α}, e ∈ B → M.IsBase B → M.IsCocircuit (M.fundCocircuit e B)- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Eproof · cited by 550
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.IsCocircuitstatement · cited by 32
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.IsBase.indepproof · cited by 22
- Matroid.dual_groundproof · cited by 9
- Matroid.IsBase.closure_eqproof · cited by 9
- Matroid.fundCocircuitstatement · cited by 9
- Matroid.IsBase.compl_isBase_dualproof · cited by 6
- Matroid.Indep.fundCircuit_isCircuitproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsNonloop.exists_mem_isCocircuitproof · cited by 0
- Matroid.Indep.exists_isCocircuit_inter_eq_memproof · cited by 0