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Theorems · Theorem · combinatorics

Matroid.indep_iff_forall_subset_not_isCircuit

∀ {α : Type u_1} {M : Matroid α} {I : Set α},
  autoParam (I ⊆ M.E) Matroid.indep_iff_forall_subset_not_isCircuit._auto_1 → (M.Indep I ↔ ∀ C ⊆ I, ¬M.IsCircuit C)
Defined in
Mathlib.Combinatorics.Matroid.Circuit
Cited by
2 results in Mathlib
Foundations
Depth 95 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.dual_rankPos_iff_exists_isCircuit · cited by 3Matroid.dual_rankPos_iff_…Matroid.ext_isCircuit · cited by 2Matroid.ext_isCircuitSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.Indep · cited by 367Matroid.IndepMatroid.IsCircuit · cited by 108Matroid.IsCircuitMatroid.indep_iff_forall_subset_not_isCircuit' · cited by 2Matroid.indep_iff_forall_…Matroid.indep_iff_forall_subs…CITED BYCITES

Cites6

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Cited by2

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