I'm reading both the French Dictionnaire égyptien by J. Champollion published in 1841 and the English edition. It's my understanding that it is the standard for decipherment. The text provides a hieroglyphic to Coptic and French or English dictionary, but appears to lack information about the methods used, such as deductive reasoning and proofs. It's my understanding the author used the Rosetta Stone, containing text in Demotic, Coptic and Ancient Greek scripts, for decipherment.
Question: does anyone know if there exist proofs with step by step inferences for these translations? I.e. a string of "if A then B", which when all taken together bring us to the translation?
As I see the work today, the dictionary inferences lack any explicit logical proofs and rather take the form of Champollion's implicit inferences. It's also my understanding he passed away before publication, so I'm curious if that is the reason for the lack of proofs.