>>> The article very clearly points out an error in the original proof.
You didn't say what error you meant here, but later you wrote this:
> The original proof used an implicit assumption, which is a problem with the proof proper
This is true, but this is not pointed out in the article at all, let alone "very clearly".
As established elsethread, the article's problem with the assumption is not it being implict or explicit, the authors simply didn't want to have to use the assumption at all.
>>> The article very clearly points out an error in the original proof.
You didn't say what error you meant here, but later you wrote this:
> The original proof used an implicit assumption, which is a problem with the proof proper
This is true, but this is not pointed out in the article at all, let alone "very clearly".
As established elsethread, the article's problem with the assumption is not it being implict or explicit, the authors simply didn't want to have to use the assumption at all.