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Make labelled Copy count computable #18

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Make labelled Copy count computable #18

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14 changes: 14 additions & 0 deletions Mathlib/Combinatorics/SimpleGraph/Copy.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -199,6 +199,16 @@ instance [Fintype {f : G →g H // Injective f}] : Fintype (G.Copy H) :=
invFun f := ⟨f.1, f.2⟩
}

instance instFintypeInjectiveHom
[Fintype V] [Fintype W] [DecidableEq V] [DecidableEq W]
[DecidableRel G.Adj] [DecidableRel H.Adj] :
Fintype {f : G →g H // Function.Injective f} :=
Fintype.ofEquiv {f : V → W // (∀ v w, G.Adj v w → H.Adj (f v) (f w)) ∧ Function.Injective f}
{ toFun := fun f => ⟨⟨f.1, fun h => f.2.1 _ _ h⟩, f.2.2⟩
invFun := fun f => ⟨f.1, ⟨fun v w h => f.1.map_adj h, f.2⟩⟩
left_inv := by intro f; rfl
right_inv := by intro f; rfl }

/-- A copy of `⊤` gives rise to an embedding of `⊤`. -/
@[simps!]
def topEmbedding (f : Copy (⊤ : SimpleGraph α) G) : (⊤ : SimpleGraph α) ↪g G :=
Expand Down Expand Up @@ -480,6 +490,10 @@ embeddings from `H` to `G`. See `SimpleGraph.copyCount` for the number of unlabe
noncomputable def labelledCopyCount (G : SimpleGraph V) (H : SimpleGraph W) : ℕ := by
classical exact Fintype.card (Copy H G)

def labelledCopyCountComputable (G : SimpleGraph V) (H : SimpleGraph W) [Fintype V] [Fintype W]
[DecidableEq V] [DecidableEq W]
[DecidableRel G.Adj] [DecidableRel H.Adj] : ℕ := Fintype.card (Copy H G)

@[simp] lemma labelledCopyCount_of_isEmpty [IsEmpty W] (G : SimpleGraph V) (H : SimpleGraph W) :
G.labelledCopyCount H = 1 := by
convert Fintype.card_unique
Expand Down
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