instFintypeElemNeighborSetOfVertsOfDecidablePredMemSet

English

The previous neighborSet_eq_of_equiv with finiteness condition asserts equality of neighbor sets.

Русский

Предыдущее утверждение neighborSet_eq_of_equiv с условием конечности требует равенства множеств соседей.

LaTeX

$$$\forall {V} {G} {v} {H} (h : G.neighborSet v \equiv H.neighborSet v) (hfin : (G.neighborSet v).Finite) : H.neighborSet v = G.neighborSet v$$$

Lean4

instance (G' : Subgraph G) [Fintype G'.verts] (v : V) [DecidablePred (· ∈ G'.neighborSet v)] :
    Fintype (G'.neighborSet v) :=
  Set.fintypeSubset G'.verts (neighborSet_subset_verts G' v)

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