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Theorems · Theorem · combinatorics

Matroid.closure_insert_congr

∀ {α : Type u_2} {M : Matroid α} {X : Set α} {e f : α},
  e ∈ M.closure (insert f X) \ M.closure X → M.closure (insert e X) = M.closure (insert f X)
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
0 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.closure · cited by 272Matroid.closureSet.insert_eq_of_mem · cited by 118Set.insert_eq_of_memSet.insert_comm · cited by 16Set.insert_commMatroid.closure_closure · cited by 14Matroid.closure_closureMatroid.closure_insert_closure_eq_closure_insert · cited by 6Matroid.closure_insert_cl…Matroid.closure_exchange · cited by 3Matroid.closure_exchangeMatroid.closure_insert_congrCITED BYCITES

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