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chore(SimpleGraph/DegreeSum): drop some DecidableEq assumptions (#10443)
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Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean

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@@ -79,16 +79,16 @@ theorem dart_card_eq_sum_degrees : Fintype.card G.Dart = ∑ v, G.degree v := by
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exact card_eq_sum_card_fiberwise (by simp)
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#align simple_graph.dart_card_eq_sum_degrees SimpleGraph.dart_card_eq_sum_degrees
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variable {G} [DecidableEq V]
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variable {G}
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theorem Dart.edge_fiber (d : G.Dart) :
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theorem Dart.edge_fiber [DecidableEq V] (d : G.Dart) :
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(univ.filter fun d' : G.Dart => d'.edge = d.edge) = {d, d.symm} :=
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Finset.ext fun d' => by simpa using dart_edge_eq_iff d' d
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#align simple_graph.dart.edge_fiber SimpleGraph.Dart.edge_fiber
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variable (G)
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theorem dart_edge_fiber_card (e : Sym2 V) (h : e ∈ G.edgeSet) :
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theorem dart_edge_fiber_card [DecidableEq V] (e : Sym2 V) (h : e ∈ G.edgeSet) :
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(univ.filter fun d : G.Dart => d.edge = e).card = 2 := by
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refine' Sym2.ind (fun v w h => _) e h
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let d : G.Dart := ⟨(v, w), h⟩
@@ -99,6 +99,7 @@ theorem dart_edge_fiber_card (e : Sym2 V) (h : e ∈ G.edgeSet) :
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#align simple_graph.dart_edge_fiber_card SimpleGraph.dart_edge_fiber_card
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theorem dart_card_eq_twice_card_edges : Fintype.card G.Dart = 2 * G.edgeFinset.card := by
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classical
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rw [← card_univ]
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rw [@card_eq_sum_card_fiberwise _ _ _ Dart.edge _ G.edgeFinset fun d _h =>
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by rw [mem_edgeFinset]; apply Dart.edge_mem]

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