User blog comment:Plain'N'Simple/A question for proof-theory experts/@comment-35392788-20191029194318/@comment-39541634-20191030070450

@P-bot

"It does not necessarily hold, but probably holds in many cases. If it can be actually verified for a specific case, the situation is much easier. "

What if we added the condition that the fundamental sequences are strictly increasing?

Would this be a sufficient condition to ensure Rpakr's statement?