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Mathlib/Combinatorics/SimpleGraph/Maps.lean

Lines changed: 10 additions & 11 deletions
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@@ -619,6 +619,16 @@ def induceUnivIso (G : SimpleGraph V) : G.induce Set.univ ≃g G where
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map_rel_iff' := by simp only [Equiv.Set.univ, Equiv.coe_fn_mk, comap_adj, Embedding.coe_subtype,
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implies_true]
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/-- The isomorphism between `completeBipartiteGraph α₁ β₁` and
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`completeBipartiteGraph α₂ β₂ ` where `α₁ ≃ α₂` and `β₁ ≃ β₂`. -/
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def completeBipartiteGraph.congr {α₁ α₂ β₁ β₂ : Type*} (hα : α₁ ≃ α₂) (hβ : β₁ ≃ β₂) :
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completeBipartiteGraph α₁ β₁ ≃g completeBipartiteGraph α₂ β₂ where
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toFun := Sum.map hα hβ
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invFun := Sum.map hα.symm hβ.symm
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left_inv _ := by simp
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right_inv _ := by simp
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map_rel_iff' := by simp
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section Finite
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variable [Fintype V] {n : ℕ}
@@ -633,17 +643,6 @@ def overFin (hc : Fintype.card V = n) : SimpleGraph (Fin n) where
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noncomputable def overFinIso (hc : Fintype.card V = n) : G ≃g G.overFin hc := by
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use Fintype.equivFinOfCardEq hc; simp [overFin]
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/-- The isomorphism between `completeBipartiteGraph α₁ β₁` and
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`completeBipartiteGraph α₂ β₂ ` where `α₁ ≃ α₂` and `β₁ ≃ β₂`. -/
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noncomputable def completeBipartiteGraph.congr {α₁ α₂ β₁ β₂ : Type*}
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[Fintype α₁] [Fintype α₂] [Fintype β₂] [Fintype β₂] (hα : α₁ ≃ α₂) (hβ : β₁ ≃ β₂) :
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completeBipartiteGraph α₁ β₁ ≃g completeBipartiteGraph α₂ β₂ where
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toFun := Sum.map hα hβ
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invFun := Sum.map hα.symm hβ.symm
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left_inv _ := by simp
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right_inv _ := by simp
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map_rel_iff' := by simp
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end Finite
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end SimpleGraph

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