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[Merged by Bors] - feat(Combinatorics/SimpleGraph): add simp lemma getVert_map for Walk.map #32102

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[Merged by Bors] - feat(Combinatorics/SimpleGraph): add simp lemma getVert_map for Walk.map #32102

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b374853
feat(Combinatorics/SimpleGraph): add simp lemma `getVert_map` for `Wa…
Nov 25, 2025
349868d
feat(Combinatorics/SimpleGraph) `getVert_map` same proof as other ope…
maix00 Nov 26, 2025
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6 changes: 6 additions & 0 deletions Mathlib/Combinatorics/SimpleGraph/Walks/Maps.lean
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Expand Up @@ -100,6 +100,12 @@ theorem edges_map : (p.map f).edges = p.edges.map (Sym2.map f) := by
@[simp]
theorem edgeSet_map : (p.map f).edgeSet = Sym2.map f '' p.edgeSet := by ext; simp

@[simp]
theorem getVert_map (i : ℕ) : (p.map f).getVert i = f (p.getVert i) := by
revert u; induction i with
| zero => simp
| succ => intro _ p; cases p <;> simp [*]

theorem map_injective_of_injective {f : G →g G'} (hinj : Function.Injective f) (u v : V) :
Function.Injective (Walk.map f : G.Walk u v → G'.Walk (f u) (f v)) := by
intro p p' h
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