Theorems · Theorem · combinatorics
Matroid.IsCircuit.eq_of_not_indep_subset
∀ {α : Type u_1} {M : Matroid α} {C X : Set α}, M.IsCircuit C → ¬M.Indep X → X ⊆ C → X = C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Indepstatement and proof · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- eq_of_le_of_not_ltproof · cited by 28
- Matroid.IsCircuit.ssubset_indepproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.eq_of_dep_subsetproof · cited by 3
- Matroid.IsCircuit.finiteproof · cited by 2
- Matroid.ext_isCircuit_not_indepproof · cited by 0