How ChangeNotifier notify the state?

Can someone give me idea how provider notify the state?

I don't want to use ChangeNotifierProvider, Can you give me a suggestion without library?

I just need better explanation with example. How provider combine InheritedWidget.

What do you think about the following example (inspired by an answer here) with an AnimatedBuilder:

import 'package:flutter/material.dart';

class MyChangeNotifier extends ChangeNotifier {
  int count = 0;

  void addOne() {
    count++;
    notifyListeners();
  }
}

class MyApp extends StatelessWidget {
  final MyChangeNotifier myChangeNotifier = MyChangeNotifier();

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        body: Center(
          child: ExampleButton(myChangeNotifier),
        ),
        floatingActionButton: FloatingActionButton(
          child: const Icon(Icons.add),
          onPressed: myChangeNotifier.addOne,
        ),
      ),
    );
  }
}

class ExampleButton extends StatelessWidget {
  final MyChangeNotifier myChangeNotifier;
  const ExampleButton(this.myChangeNotifier, {Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return AnimatedBuilder(
        animation: myChangeNotifier,
        builder: (context, child) {
          return OutlinedButton(
              onPressed: myChangeNotifier.addOne,
              child: Text(
                'Tap me - or the floating button\n\n${myChangeNotifier.count}',
                textAlign: TextAlign.center,
              ));
        });
  }
}

void main() => runApp(MyApp());

The ChangeNotifier implements the Listenable class. You can see here how to listen to that Listenable, for example with an AnimatedBuilder (what my code does). A ChangeNotifyProvider (I know, you don't want that) would also implement that for you and notify your widgets lower in the widget tree about changes.