Here is the steps:

1. save the docker image app_image:456 to a file

   docker save -o app_image456.tar app_image:456

2. Take checksum of the image file

   md5sum app_image456.tar This will produce the checksum of the image

Now, create a docker image using docker file (FROM curated_image:123, the one used to create app_image:456), but give different tag. Then do step 1 and 2 again using this docker image & compare the checksum. If the checksum the same then you have same content.