must have a corresponding image in Υ ′ under any isomorphism η, preserving their adjacency and distances from Γ(G ′ , H ′ , β). Therefore, the restriction η r of η to the extended reaction center Ψ r is also an isomorphism from Ψ r to Ψ ′ r , since these subgraphs are unique w.r.t the inclusion of the reaction centers and the closure under vertices at distance at most r from them, which holds for every r > 0 as required.