AngularJS use custom services in custom providers - angularjs

Question

I have a simple question about the dependency injection in Angular. I create custom services in order to use them within each other. Unfortunately I receive errors the way I was trying it. This is my Code:
var myApp = angular.module('app', []);
myApp.service('$service1', ['$rootScope', function($rootScope) {
this.test = function() {
console.log('service1');
};
}]);
myApp.provider('$service2', ['$service1', function($service1) {
var service = 'service2';
this.registerService = function(mytext) {
service = mytext;
};
this.$get = function() {
var that = {};
that.test = function() {
console.log(service);
};
return that;
};
}]);
myApp.config(['$service2Provider', function($service2Provider) {
$service2Provider.registerService('changed service2');
}]);
myApp.controller('AppCtrl', ['$rootScope', '$service1', '$service2',
function($rootScope, $service1, $service2) {
$service1.test();
$service2.test();
}]);
Error: [$injector:modulerr] Failed to instantiate module app due to:
[$injector:unpr] Unknown provider: $service1
http://errors.angularjs.org/1.2.0-rc.2/$injector/unpr?p0=%24service1
If you remove the dependency of $servic1 in $service2 it will work, but why?

Answer 1

The code is mostly right, except you have to inject service dependencies in $get, not in the provider constructor function, like this:
myApp.provider('$service2', function() {
var service = 'service2';
this.registerService = function(mytext) {
service = mytext;
};
this.$get = ['$service1', function($service1) {
var that = {};
that.test = function() {
console.log(service);
};
return that;
}];
});

Answer 2

It appears that provider can not inject such a dependency. If you rewrite $service2 using a factory, it works:
myApp.factory('$service2', ['$service1', function($service1) {
var that = {};
that.test = function() {
$service1.test();
console.log('service2');
};
return that;
}]);
See this plunker: http://plnkr.co/edit/JXViJq?p=preview
Also I believe that service names starting with a $ a reserved for AngularJS and its extensions. Use names without the $ at the beginning for services defined by your application.