The answer above by @schroeder is spot-on (+1). It is impossible for you as the recipient to prove that you didn't receive an email. However, the sender does have the ability to prove that they sent an email, and that the mail server that handles incoming mail for your domain received it, and that this mail server acknowledged receipt.
The diagram below shows the journey that an email message makes from the sender to the recipient:
The sender's outgoing SMTP mail server will typically log every delivery attempt. When the message is handed off from the sender's outgoing SMTP server to the recipient's incoming MX server, the incoming mail server will acknowledge receipt with a
2xx response and will usually include a unique identifier that it assigned to the message in this response. The sender's outgoing SMTP server will typically include all of this in its logs. So, if there is any question as to whether a message was sent, and whether it was delivered (at least to the recipient's incoming MX server for their domain), this should all be in the sender's outgoing SMTP server logs.
Of course, even if the recipient's incoming MX server received the message, it is still possible that the recipient may not receive the message in their inbox. This can happen if the recipient's incoming MX server dropped the message, or treated it as spam, or otherwise mishandled the message. But, at least the sender can show that they sent the message, and that the message made it to the recipient's incoming MX server, and that the recipient's incoming MX server acknowledged receipt of the message. If the recipient never received the message in their inbox, then the recipient can go to the admin of their incoming MX server, armed with the logs provided by the sender, and ask the admin to track down the missing message, and ask for an explanation.
As you can see, this all hinges on the sender being able to access their outgoing SMTP server logs. If the sender outsources their outgoing email to a third party provider, it might be difficult to get the provider to pull these log records, as this is typically beyond the level of service that most mail providers offer (at least at the individual/SOHO/SMB level). However, an outgoing SMTP service such as UltraSMTP, makes these log records available to end users through a self-serve web interface, so that end users can get the information they need themselves to track down problems with non-received messages. [FD, I am the developer.]