Theorems · Theorem · combinatorics
Matroid.contract_isNonloop_iff
∀ {α : Type u_1} {M : Matroid α} {e : α} {C : Set α}, (M.contract C).IsNonloop e ↔ e ∈ M.E \ M.closure C- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.closurestatement and proof · cited by 272
- Matroid.contractstatement and proof · cited by 103
- Matroid.IsNonloopstatement · cited by 65
- Matroid.loopsproof · cited by 52
- Matroid.subset_closureproof · cited by 23
- Matroid.closure_inter_groundproof · cited by 22
- Matroid.contract_groundproof · cited by 12
- Matroid.contract_loops_eqproof · cited by 4
- Matroid.isNonloop_iff_mem_compl_loopsproof · cited by 2
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