Theorems · Theorem · combinatorics
Matroid.ext_isCircuit
∀ {α : Type u_1} {M₁ M₂ : Matroid α},
M₁.E = M₂.E → (∀ ⦃C : Set α⦄, C ⊆ M₁.E → (M₁.IsCircuit C ↔ M₂.IsCircuit C)) → M₁ = M₂- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 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.
Cites10
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.Estatement and proof · cited by 550
- Matroid.Indepproof · cited by 367
- LE.le.trans_eqproof · cited by 328
- emproof · cited by 115
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.ext_indepproof · cited by 15
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Matroid.indep_iff_forall_subset_not_isCircuitproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.ext_isCircuit_not_indepproof · cited by 0
- Matroid.ext_iff_isCircuitproof · cited by 0