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Theorems · Theorem · combinatorics

Matroid.not_isLoop_iff

∀ {α : Type u_1} {M : Matroid α} {e : α},
  autoParam (e ∈ M.E) Matroid.not_isLoop_iff._auto_1 → (¬M.IsLoop e ↔ M.IsNonloop e)
Defined in
Mathlib.Combinatorics.Matroid.Loop
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
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Around this declaration

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

Matroid.isNonloop_of_loopless · cited by 6Matroid.isNonloop_of_loop…Matroid.Indep.isNonloop_of_mem · cited by 5Indep.isNonloop_of_memMatroid.IsCocircuit.isNonloop_of_mem · cited by 1IsCocircuit.isNonloop_of_…Matroid.loopless_iff_forall_not_isLoop · cited by 1Matroid.loopless_iff_fora…Matroid.not_isNonloop_iff · cited by 0Matroid.not_isNonloop_iffSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.IsNonloop · cited by 65Matroid.IsNonloopMatroid.IsLoop · cited by 55Matroid.IsLoopMatroid.IsNonloop.not_isLoop · cited by 8IsNonloop.not_isLoopMatroid.not_isLoop_iffCITED BYCITES

Cites6

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Cited by5

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