Assumptions with the same name clash, should be based off of proof node IDs which are globally unique. Example:  Proof: https://james-oswald.github.io/lazyslate/?proof=N4Igdg9gJgpgziAXAbVASykgDAGnAQwFsYkQA5ImAQRDxgA8AHAJ3jjQjFJrwCsBXOABc0AMzQBjfCM6l8cOP2K0QjCOxldEoekgCsWAIx4AnkgBMevQF9rOdJkTGCyxOUo8QDFmw5aQAEIqAsJiktJ+cgpKJHhqGpHaILqIAOyGuCBmiJYALLb2IBgWeGCUpOYq3qwKiSAAFPhgUAAEVC0BAJTBgiLiUppyzQCSKvFog0kpegCcABymSLkAzHO2ALp4ADZoYADWCCjIuOabyMan69ZAA
Assumptions with the same name clash, should be based off of proof node IDs which are globally unique.
Example:

Proof:
https://james-oswald.github.io/lazyslate/?proof=N4Igdg9gJgpgziAXAbVASykgDAGnAQwFsYkQA5ImAQRDxgA8AHAJ3jjQjFJrwCsBXOABc0AMzQBjfCM6l8cOP2K0QjCOxldEoekgCsWAIx4AnkgBMevQF9rOdJkTGCyxOUo8QDFmw5aQAEIqAsJiktJ+cgpKJHhqGpHaILqIAOyGuCBmiJYALLb2IBgWeGCUpOYq3qwKiSAAFPhgUAAEVC0BAJTBgiLiUppyzQCSKvFog0kpegCcABymSLkAzHO2ALp4ADZoYADWCCjIuOabyMan69ZAA