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feat(Combinatorics/SimpleGraph): add lemma Walk.not_nil_iff_ne_nil #37575

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feat(Combinatorics/SimpleGraph): add lemma Walk.not_nil_iff_ne_nil #37575

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2 changes: 2 additions & 0 deletions Mathlib/Combinatorics/SimpleGraph/Walk/Basic.lean
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Expand Up @@ -381,6 +381,8 @@ lemma not_nil_iff {p : G.Walk v w} :
lemma nil_iff_eq_nil : ∀ {p : G.Walk v v}, p.Nil ↔ p = nil
| .nil | .cons _ _ => by simp

lemma not_nil_iff_ne_nil {p : G.Walk v v} : ¬ p.Nil ↔ p ≠ nil := by rw [nil_iff_eq_nil]

alias ⟨Nil.eq_nil, _⟩ := nil_iff_eq_nil

lemma nil_of_subsingleton [Subsingleton V] (p : G.Walk v w) : p.Nil :=
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