PS: According to Frequently Asked Questions about Intel® Graphics Drivers Support for... the HD4000 apparently should support Miracast.
But then why does the DxDiag.txt say that Miracast is not supported by the graphics driver and resulting in Miracast not being available for the HD4000 on Windows 10?
This message was posted on behalf of Intel Corporation
Thank you for joining the Graphics Community. I am sorry to hear you are having issues with Miracast.
Based in our information, Windows® 10 and Intel® HD Graphics 4000 support Miracast. But, since this a Microsoft technology the best thing to do is to report this behavior with their support, find the contact information here: https://support.microsoft.com/en-us