Theorems · Theorem · combinatorics
Matroid.IsNonloop.closure_eq_closure_iff_eq_or_dep
∀ {α : Type u_1} {M : Matroid α} {e f : α},
M.IsNonloop e → M.IsNonloop f → (M.closure {e} = M.closure {f} ↔ e = f ∨ ¬M.Indep {e, f})- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 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
- eq_or_neproof · cited by 1,117
- Matroid.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.closurestatement · cited by 272
- Matroid.IsCircuitproof · cited by 108
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.indep_singletonproof · cited by 12
- Matroid.IsNonloop.mem_groundproof · cited by 6
- Set.pair_sdiff_leftproof · cited by 4
- Set.pair_sdiff_rightproof · cited by 3
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