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Theorems · Theorem · combinatorics

Matroid.IsNonloop.not_isLoop

∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsNonloop e → ¬M.IsLoop e
Defined in
Mathlib.Combinatorics.Matroid.Loop
Cited by
8 results in Mathlib
Foundations
Depth 9 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.not_isLoop_iff · cited by 5Matroid.not_isLoop_iffMatroid.IsColoop.notMem_isCircuit · cited by 3IsColoop.notMem_isCircuitMatroid.not_isLoop · cited by 1Matroid.not_isLoopMatroid.eRk_eq_zero_iff' · cited by 1Matroid.eRk_eq_zero_iff'Matroid.IsNonloop.isNonloop_of_mem_closure · cited by 1IsNonloop.isNonloop_of_me…Matroid.loopless_iff_forall_isNonloop · cited by 1Matroid.loopless_iff_fora…Matroid.IsLoop.not_isColoop · cited by 1IsLoop.not_isColoopMatroid.IsLoop.not_isNonloop · cited by 0IsLoop.not_isNonloopMatroid · cited by 1258MatroidMatroid.IsNonloop · cited by 65Matroid.IsNonloopMatroid.IsLoop · cited by 55Matroid.IsLoopIsNonloop.not_isLoopCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.