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Theorems · Theorem · combinatorics

Matroid.insert_isBase_of_insert_indep

∀ {α : Type u_1} {M : Matroid α} {I : Set α} {e f : α},
  e ∉ I → f ∉ I → M.IsBase (insert e I) → M.Indep (insert f I) → M.IsBase (insert f I)
Defined in
Mathlib.Combinatorics.Matroid.Basic
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 53352SetMatroid · cited by 1258Matroideq_or_ne · cited by 1117eq_or_neMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBase · cited by 239Matroid.IsBaseSet.sdiff_singleton_eq_self · cited by 38Set.sdiff_singleton_eq_se…Set.insert_sdiff_of_mem · cited by 22Set.insert_sdiff_of_memMatroid.IsBase.exchange_isBase_of_indep · cited by 3IsBase.exchange_isBase_of…Matroid.insert_isBase_of_inse…CITED BYCITES

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