Is this correct?

Smaller diameter wires going into top of panel go to the smaller remote breaker for a/c.
Just does not appear to be a correct installation to me. Thanks in advance for your answers.

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Brian,
Do you have any pictures of the feeder lugs on the 1st picture? From the angle of this picture it appears that the wires you are talking about are double lugged with the main feed wires. Unless the lugs are approved for double lugging it is not allowed.

Appears To be a double tap as well. I concur with David

Also the wires from the service wire terminals are not protected at all or protected by an oversized OCPD until they reach the breakered disconnect.

Agreed. Even if those lugs are rated for multiple conductors, the feeders shouldn’t be tapped in before the service disconnect.

I agree. Double tap at the service entrance is a no-no. There is no way to disconnect power to that sub panel. You didn’t mention if the sub panel is bonded. That is another consideration to mention.