let book = Map [(1, ["daniel"; "martin"; "bella"]); (2,   ["daniel"; "martin"]); (3, ["bella"])];;

let words = book |> Map.toList |> List.map snd |> List.concat |> Set.ofList

let inverseBook =
  [ for word in words do
      let pages =
        book
        |> Map.toList
        |> List.choose (fun (page, pageWords) -> if List.exists ((=) word) pageWords then Some page else None)
      yield word, pages ]