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Theorems · Theorem · combinatorics

SimpleGraph.Walk.Nil.eq_nil

∀ {V : Type u} {G : SimpleGraph V} {v : V} {p : G.Walk v v}, p.Nil → p = SimpleGraph.Walk.nil

Alias of the reverse direction of SimpleGraph.Walk.eq_nil_iff_nil. A walk with its endpoints defeq is Nil if and only if it is equal to nil.

Defined in
Mathlib.Combinatorics.SimpleGraph.Walk.Basic
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.Walk.IsCycle.not_nil · cited by 14IsCycle.not_nilSimpleGraph.Walk.IsCircuit.not_nil · cited by 0IsCircuit.not_nilSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Walk · cited by 915SimpleGraph.WalkSimpleGraph.Walk.Nil · cited by 102Walk.NilSimpleGraph.Walk.eq_nil_iff_nil · cited by 6Walk.eq_nil_iff_nilNil.eq_nilCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.