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golf minDegree_le_degree
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Mathlib/Combinatorics/SimpleGraph/Finite.lean

Lines changed: 2 additions & 4 deletions
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@@ -400,10 +400,8 @@ theorem exists_minimal_degree_vertex [DecidableRel G.Adj] [Nonempty V] :
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grind [minDegree, WithTop.untopD_coe, min_mem_image_coe <| univ_nonempty.image (G.degree ·)]
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/-- The minimum degree in the graph is at most the degree of any particular vertex. -/
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theorem minDegree_le_degree [DecidableRel G.Adj] (v : V) : G.minDegree ≤ G.degree v := by
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obtain ⟨t, ht⟩ := Finset.min_of_mem (mem_image_of_mem (fun v => G.degree v) (mem_univ v))
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have := Finset.min_le_of_eq (mem_image_of_mem _ (mem_univ v)) ht
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rwa [minDegree, ht]
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theorem minDegree_le_degree [DecidableRel G.Adj] (v : V) : G.minDegree ≤ G.degree v :=
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WithTop.untopD_le <| Finset.min_le <| mem_image_of_mem (G.degree ·) <| mem_univ v
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/-- In a nonempty graph, if `k` is at most the degree of every vertex, it is at most the minimum
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degree. Note the assumption that the graph is nonempty is necessary as long as `G.minDegree` is

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