Theorems · Theorem · combinatorics
Matroid.restrict_indep_iff
∀ {α : Type u_1} {M : Matroid α} {R I : Set α}, (M.restrict R).Indep I ↔ M.Indep I ∧ I ⊆ R- Cited by
- 13 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 367
- Matroid.restrictstatement · cited by 111
Cited by13
Results whose statement or proof uses this declaration.
- Matroid.restrict_closure_eq'proof · cited by 9
- Matroid.delete_indep_iffproof · cited by 7
- Matroid.restrict_isNonloop_iffproof · cited by 3
- Matroid.Indep.indep_restrict_of_subsetproof · cited by 2
- Matroid.removeLoops_indep_eqproof · cited by 2
- Matroid.Indep.of_restrictproof · cited by 1
- Matroid.contract_restrict_eq_restrict_contractproof · cited by 1
- Matroid.uniqueBaseOn_indep_iff'proof · cited by 1
- Matroid.restrict_dep_iffproof · cited by 1
- Matroid.restrict_eq_freeOn_iffproof · cited by 1
- Matroid.Indep.exists_insert_of_not_isBasisproof · cited by 0
- Matroid.uniqueBaseOn_indep_iffproof · cited by 0