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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -284,15 +284,12 @@ theorem mapDomain_notin_range {f : α → β} (x : α →₀ M) (a : β) (h : a
284284@[simp] lemma mapDomain_id : mapDomain id v = v := sum_single _
285285@[simp] lemma mapDomain_fun_id : mapDomain (fun x ↦ x) v = v := sum_single _
286286
287+ lemma mapDomain_fun_comp (f : α → β) (g : β → γ) :
288+ mapDomain (fun a ↦ g (f a)) v = mapDomain g (mapDomain f v) := by
289+ simp [mapDomain, sum_sum_index]
290+
287291theorem mapDomain_comp {f : α → β} {g : β → γ} :
288- mapDomain (g ∘ f) v = mapDomain g (mapDomain f v) := by
289- refine ((sum_sum_index ?_ ?_).trans ?_).symm
290- · intro
291- exact single_zero _
292- · intro
293- exact single_add _
294- refine sum_congr fun _ _ => sum_single_index ?_
295- exact single_zero _
292+ mapDomain (g ∘ f) v = mapDomain g (mapDomain f v) := mapDomain_fun_comp f g
296293
297294@[simp]
298295theorem mapDomain_single {f : α → β} {a : α} {b : M} : mapDomain f (single a b) = single (f a) b :=
Original file line number Diff line number Diff line change @@ -253,8 +253,7 @@ lemma map_id [Finite X] : map (_root_.id : X → X) (M := M) = _root_.id := by
253253
254254lemma map_comp [Finite X] [Finite Y] [Finite Z] (g : Y → Z) (f : X → Y) :
255255 map (g.comp f) (M := M) = (map g).comp (map f) := by
256- ext s
257- simp [map, Finsupp.mapDomain_comp]
256+ ext s; simp [map, Finsupp.mapDomain_fun_comp]
258257
259258end
260259
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