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Theorems · Theorem · combinatorics

Matroid.Indep.of_contract

∀ {α : Type u_1} {M : Matroid α} {I C : Set α}, (M.contract C).Indep I → M.Indep I
Defined in
Mathlib.Combinatorics.Matroid.Minor.Contract
Cited by
2 results in Mathlib
Foundations
Depth 103 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.of_isMinor · cited by 1Indep.of_isMinorMatroid.IsNonloop.of_contract · cited by 1IsNonloop.of_contractSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.Indep · cited by 367Matroid.IndepSet.subset_union_left · cited by 142Set.subset_union_leftMatroid.contract · cited by 103Matroid.contractMatroid.Indep.subset · cited by 42Indep.subsetMatroid.exists_isBasis' · cited by 30Matroid.exists_isBasis'Matroid.IsBasis'.contract_indep_iff · cited by 4IsBasis'.contract_indep_i…Indep.of_contractCITED BYCITES

Cites8

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.