Theorems · Theorem · combinatorics
Matroid.IsColoop.insert_indep_of_indep
∀ {α : Type u_1} {M : Matroid α} {e : α} {I : Set α}, M.IsColoop e → M.Indep I → M.Indep (insert e I)- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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 and proof · cited by 367
- Set.insert_eq_of_memproof · cited by 118
- emproof · cited by 115
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.IsColoop.mem_groundproof · cited by 6
- Matroid.Indep.notMem_closure_iff_of_notMemproof · cited by 2
- Matroid.IsColoop.notMem_closure_of_notMemproof · cited by 1
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