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Theorems · Theorem · combinatorics

Matroid.IsBasis.diff_subset_loops_contract

Deprecated since 2026-06-03Use Matroid.IsBasis.sdiff_subset_loops_contract instead.

∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis I X → X \ I ⊆ (M.contract I).loops

Alias of Matroid.IsBasis.sdiff_subset_loops_contract.

Defined in
Mathlib.Combinatorics.Matroid.Minor.Contract
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Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.contract · cited by 103Matroid.contractMatroid.loops · cited by 52Matroid.loopsMatroid.IsBasis.sdiff_subset_loops_contract · cited by 1IsBasis.sdiff_subset_loop…IsBasis.diff_subset_loops_con…CITED BYCITES

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