Over 40,000 lead seals from the early Byzantine Empire remain today.
Conclusion (thus)
The number of documents sealed with a lead seal was many times the number of remaining lead seals.
Evidence
There are about 40,000 lead seals that remain.
Most lead seals would serve their purpose when the document was opened, and once they had served their purpose, most lead lead seals would be recast (i.e. recycled so that they could be used again).
Evaluate
This is a tough conclusion to disagree with. It's just saying that, .
Let's just say "3 times as many" to make this more concrete. That means that the author is claiming that if we've found 40,000 remaining lead seals, then there must have been at least 120,000 documents sealed with lead seals.
Why?
Because the author is assuming that lead seals got reused, because it cost money to make each one. She is thinking that they would make a lead seal, attach it to a document, that document would be opened (and thus the seal had served its purpose), and then the seal would be recast to be used again.
If we were trying to fight the conclusion, we'd either have to say that a ton of these 40,000 lead seals that remain were never attached to a document, or we'd have to say that they were attached to a document but weren't recycled multiple times and used on several documents.
Goal
Since we want to strengthen, we want to counter those possible objections. We want to be more convinced that the remaining seals WERE attached to documents; the seals attached to documents WERE recycled multiple times.