Roteamento Angular 2.0 - TS 2305… não possui membro exportado 'ModulewithProviders'

Eu estou seguindo umtutorial angular 2.0 no oficial js angularlocal e ficou preso no final do exercício de roteamento. O código funcionou da última vez, mas outro dia quando eu aperteinpm start'no node.js cmd novamente, o "error: TS 2305 ... não possui membro exportado 'ModulewithProviders'"apareceu, apesar de todos os arquivos terem sido intocados.

Aqui está o código na mesma pasta do aplicativo:

main.ts:

import {platformBrowserDynamic} from '@angular/platform-browser-dynamic';
import {AppModule} from './app.module';
platformBrowserDynamic().bootstrapModule(AppModule);

app.module.ts

import {NgModule} from '@angular/core';
import {BrowserModule} from '@angular/platform-browser';
import {AppComponent} from './app.component';
import {HeroesComponent} from './heroes.component';
import {DashboardComponent} from './dashboard.component';
import {routing} from './app.routing';
import {FormsModule} from '@angular/forms';

@NgModule({
    imports: [BrowserModule,FormsModule,routing],
    declarations: [AppComponent, HeroesComponent, DashboardComponent],
    bootstrap: [AppComponent],
})

export class AppModule {}

app.component.ts

import {Component} from '@angular/core';

@Component({
    selector: 'my-app',
    template: `
        <h1>{{title}}</h1>
        <nav>
        <a routerLink="/heroes">Heroes</a>
        <a routerLink="/dashboard">Dashboard</a>
        </nav>
        <router-outlet></router-outlet>
    `
})
export class AppComponent{
    title: string = "Tour of heroes"
}

heroes.component.ts

import {Component} from '@angular/core';

@Component({
    selector: 'hero-component',
    template: `<div>Heroes </div>`
})
export class HeroComponent{};

dashboard.component.ts

import {Component} from '@angular/core';

@Component({
    selector: 'dashboard-component',
    template: `<div>Dashboard </div>`
})
export class DashboardComponent{};

app.routing.ts

import { ModulewithProviders } from '@angular/core';
import {Routes, RouterModule} from '@angular/router';
import {HeroesComponent} from './heroes.component';
import {DashboardComponent} from './dashboard.component';

const appRoutes: Routes = [
    {
        path: 'heroes',
        component: HeroesComponent
    },
    {
        path: 'dashboard',
        component: DashboardComponent
    },
    {
        path: '',
        redirectTo: '/dashboard',
        pathMatch: 'full'
    }
]
export const routing: ModulewithProviders = RouterModule.forRoot(appRoutes);

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