typescriptでreduxのstateにアクセス可能でかつreact-routerのRouteに指定できるコンポーネントを作りたい

Question

まずはコードをご確認下さい

import * as React from 'react';
import {BrowserRouter as Router, Route, Link, withRouter} from 'react-router-dom';
import {RouteComponentProps} from 'react-router';
import {connect} from 'react-redux';

interface TestProps {
  state: Object;
}
const Index = (props: RouteComponentProps<undefined>) => (<h1>index</h1>);
const About = (props: RouteComponentProps<undefined>) => (<h1>about</h1>);

const AccessReduxStore = (props: RouteComponentProps<{}> & TestProps) => (<h1>access to redux store</h1>);
const mapStateToProps = (state: {}): TestProps => {
  return {
    state
  };
};

const ReduxAccessWithRouter = withRouter<TestProps>(connect(mapStateToProps)(AccessReduxStore));

class App extends React.Component<{}, {}> {
  render() {
    return (
      <div className="App">
        
        <Router>
          <div>
          <a> <Link to={'/'} >Index</Link></a>
          <a> <Link to={'/about'} >about</Link></a>
          <a> <Link to={'/access'} >access</Link></a>
          <Route exact={true} path={'/'} component={Index} />
          <Route  path={'/about'} component={About} />

          // error箇所
          <Route  path={'/access'} component={ReduxAccessWithRouter} />
          </div>
        </Router>
      </div>
    );
  }
}

export default App;

表題のとおりです。このコードの問題はReduxAccessWithRouterを作る部分の箇所で
react-routerのマニュアルに寄るとwithRouter(connect(...)(MyComponent)) という変換で目的のコンポーネントを作れるかと思ったんですが以下のようなエラーが出ます

./src/App.tsx
(19,78): error TS2345: Argument of type '(props: RouteComponentProps<{}> & TestProps) => Element' is not assignable to parameter of type 'Component<DispatchProp<any> & TestProps>'.
  Type '(props: RouteComponentProps<{}> & TestProps) => Element' is not assignable to type 'StatelessComponent<DispatchProp<any> & TestProps>'.
    Types of parameters 'props' and 'props' are incompatible.
      Type 'DispatchProp<any> & TestProps & { children?: ReactNode; }' is not assignable to type 'RouteComponentProps<{}> & TestProps'.
        Type 'DispatchProp<any> & TestProps & { children?: ReactNode; }' is not assignable to type 'RouteComponentProps<{}>'.
          Property 'match' is missing in type 'DispatchProp<any> & TestProps & { children?: ReactNode; }'.

AccessReduxStoreのpropsの定義の仕方が問題なのかと思いますが、どうしても上手く生きません。
ご教授お願い致します。

Answer 1

変更箇所のコードだけ纏めます

interface TestProps extends RouteComponentProps<{}> { 
  state: Object;
}
const AccessReduxStore = (props: TestProps) => 
  (<h1>access to redux store{JSON.stringify(props.state)}</h1>);

const mapStateToProps = (state: {}, ownProps: TestProps): TestProps => {
  return {
    state,
    ...ownProps
  };
};

const ReduxAccessWithRouter = withRouter(connect(mapStateToProps)(AccessReduxStore));