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Theorems · Theorem · combinatorics

Matroid.IsBasis.isBasis_union

∀ {α : Type u_1} {M : Matroid α} {I X Y : Set α}, M.IsBasis I X → M.IsBasis I Y → M.IsBasis I (X ∪ Y)
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.Indep.closure_eq_setOfPred_isBasis_insert · cited by 6Indep.closure_eq_setOfPre…Matroid.IsFlat.iInter · cited by 1IsFlat.iInterSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.IsBasis.indep · cited by 51IsBasis.indepSet.union_self · cited by 32Set.union_selfMatroid.IsBasis.union_isBasis_union · cited by 3IsBasis.union_isBasis_uni…IsBasis.isBasis_unionCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.