Entity Framework 6 (code first) Add-Migration puts wrong provider to the edmx schema

Question

I have a project which is originally used System.Data.SqlServerCe.4.0 (MSSQL Compact Edition 4.0) data provider. Then I've made a branch, changed config file and references for System.Data.SqlClient (MSSQL provider), uninstalled EntityFramework for MSSQLCE nuget package. Everything in the branch project works fine except two things: Add-Migration and Database seed script fail with the next error:

Schema specified is not valid. Errors: (0,0) : error 0175: The ADO.NET provider with invariant name 'System.Data.SqlServerCe.4.0' is either not registered in the machine or application config file, or could not be loaded

I've tried to find the source of the issue and finally found that EDMX schema, which is stored in the __MigrationHistory of the MSSQL project database, contains the next line:

<Schema Namespace="CodeFirstDatabaseSchema" Provider="System.Data.SqlServerCe.4.0" ProviderManifestToken="4.0" Alias="Self" xmlns:customannotation="http://schemas.microsoft.com/ado/2013/11/edm/customannotation" xmlns="http://schemas.microsoft.com/ado/2009/11/edm/ssdl">

But I don't understand, why it is generated with the Provider="System.Data.SqlServerCe.4.0" option ? I've checked that my branch project doesn't have any file, which contains SqlServerCe substring (did file search in OS). I've tried to reinstall EntityFramework NuGet package, doesn't help as well.

App.Config:

<?xml version="1.0" encoding="utf-8"?>
<configuration>
  <configSections>
    <section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
  </configSections>
  <startup>
    <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
  </startup>
  <entityFramework>
    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.SqlConnectionFactory, EntityFramework" />
    <providers>
      <provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
    </providers>
  </entityFramework>
  <connectionStrings>
    <add name="AppDBContext" connectionString="Data Source=.\SQLEXPRESS;Initial Catalog=AnalyticDB;Persist Security Info=True;Trusted_Connection=Yes;MultipleActiveResultSets=True" providerName="System.Data.SqlClient" />
  </connectionStrings>
</configuration>

EF version: 6.1.2

Thanks!