Theorems · Theorem · combinatorics
Matroid.IsCircuit.contract_dep_of_not_subset
∀ {α : Type u_1} {M : Matroid α} {K : Set α}, M.IsCircuit K → ∀ {C : Set α}, ¬K ⊆ C → (M.contract C).Dep (K \ C)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Set.inter_subset_rightproof · cited by 329
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.contractstatement and proof · cited by 103
- Matroid.Depstatement and proof · cited by 76
- Set.inter_union_sdiffproof · cited by 23
- Set.sdiff_inter_self_eq_sdiffproof · cited by 16
- LE.le.ssubset_of_neproof · cited by 16
- disjoint_sdiff_sdiffproof · cited by 6
- Matroid.contract_contractproof · cited by 5
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
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