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Theorems · Theorem · combinatorics

Matroid.contract_isLoop_iff_mem_closure

∀ {α : Type u_1} {M : Matroid α} {e : α} {C : Set α}, (M.contract C).IsLoop e ↔ e ∈ M.closure C ∧ e ∉ C
Defined in
Mathlib.Combinatorics.Matroid.Minor.Contract
Cited by
0 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetDisjoint · cited by 2201DisjointMatroid · cited by 1258MatroidMatroid.closure · cited by 272Matroid.closureMatroid.contract · cited by 103Matroid.contractMatroid.IsBasis' · cited by 101Matroid.IsBasis'Matroid.Dep · cited by 76Matroid.DepMatroid.IsLoop · cited by 55Matroid.IsLoopMatroid.exists_isBasis' · cited by 30Matroid.exists_isBasis'Matroid.IsBasis'.indep · cited by 27IsBasis'.indepMatroid.IsBasis'.subset · cited by 25IsBasis'.subsetSet.singleton_union · cited by 22Set.singleton_unionMatroid.IsBasis'.closure_eq_closure · cited by 12IsBasis'.closure_eq_closu…Matroid.singleton_dep · cited by 8Matroid.singleton_depMatroid.IsBasis'.contract_eq_contract_delete · cited by 5IsBasis'.contract_eq_cont…Matroid.contract_isLoop_iff_m…CITED BYCITES

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