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Theorems · Theorem · combinatorics

Matroid.IsBasis.isBasis_of_closure_eq_closure

∀ {α : Type u_2} {M : Matroid α} {X Y I : Set α},
  M.IsBasis I X →
    I ⊆ Y →
      M.closure X = M.closure Y →
        autoParam (Y ⊆ M.E) Matroid.IsBasis.isBasis_of_closure_eq_closure._auto_1 → M.IsBasis I Y
Defined in
Mathlib.Combinatorics.Matroid.Closure
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Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.closure · cited by 272Matroid.closureMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.IsBasis.indep · cited by 51IsBasis.indepMatroid.subset_closure · cited by 23Matroid.subset_closureMatroid.IsBasis.closure_eq_closure · cited by 13IsBasis.closure_eq_closureMatroid.Indep.isBasis_of_subset_of_subset_closure · cited by 8Indep.isBasis_of_subset_o…IsBasis.isBasis_of_closure_eq…CITED BYCITES

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