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Artifact used (ex. androidx.appcompat:appcompat:1.0.0-alpha1):
Version used: androidx.core:core:1.8.0
Theme used: Any
Devices/Android versions reproduced on: Any

This might be an build tool issue.

Steps to reproduce:

1. Create an android app with AndroidX support.
2. Create an android lib module with AndroidX support.
3. Add the following to your library project's AndroidManifest.xml:

        <provider
            android:name="androidx.core.content.FileProvider"
            android:authorities="${applicationId}.provider"
            android:exported="false"
            android:grantUriPermissions="true">
            <meta-data
                android:name="android.support.FILE_PROVIDER_PATHS"
                android:resource="@xml/lib_provider_paths" />
        </provider>

And lib_provider_paths.xml to your library project's res folder:

<?xml version="1.0" encoding="utf-8"?>
<paths>
    <external-path name="external_files" path="."/>
</paths>

4. Add the following to your application's AndroidManifest.xml:

        <provider
            android:name="androidx.core.content.FileProvider"
            android:authorities="${applicationId}.provider"
            android:exported="false"
            android:grantUriPermissions="true">
            <meta-data
                android:name="android.support.FILE_PROVIDER_PATHS"
                android:resource="@xml/app_provider_paths" />
        </provider>

and And app_provider_paths.xml to your library project's res folder:

<?xml version="1.0" encoding="utf-8"?>
<paths>
    <cache-path
        name="downloads"
        path="/" />
    <external-path name="external_files" path="."/>
</paths>

5. Run ./gradlew assumbleDebug at project directory.

Result:

1. Gradle will fail with error:

<project_path>/app/src/debug/AndroidManifest.xml Error:
        Attribute provider#androidx.core.content.FileProvider@authorities value=(com.mycompany.myapp.fileProvider) from (unknown)
        is also present at [:lib] AndroidManifest.xml:20:13-60 value=(com.mycompany.myapp.fileProvider.
        Suggestion: add 'tools:replace="android:authorities"' to <provider> element at AndroidManifest.xml:455:9-463:20 to override.
<project_path>/app/src/debug/AndroidManifest.xml:30:17-59 Error:
        Attribute meta-data#android.support.FILE_PROVIDER_PATHS@resource value=(@xml/app_provider_paths) from [:app] AndroidManifest.xml:30:17-59
        is also present at [:lib] AndroidManifest.xml:25:17-55 value=(@xml/lib_provider_paths).
        Suggestion: add 'tools:replace="android:resource"' to <meta-data> element at AndroidManifest.xml to override.

See http://g.co/androidstudio/manifest-merger for more information about the manifest merger.

2. Provided link break with "Invalid Dynamic Link - Blocked", but this is not the point.
3. According to the provided link: Error 1 Should not be raise because these two nodes are identical. Error 2 would raise, but it is a bit stupid to raise such error and tell developer to add 'tools:replace="android:resource"' to override. Developers have to merge @xml/app_provider_paths and @xml/lib_provider_paths manually to make their apps works correctly. A better solution would be the Gradle or Android build plugin merge the XML for developer, at least specially handled by the build tool for this case.