When it comes to numbering results in a mathematical publication, I'm aware of two methods:

Joint numbering:

*Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc.*Separate numbering:

*Thm. 1, Prop. 1, Thm. 2, Lem. 1, etc.*

Every piece of writting advice I have encountered advocates the use of 1. over 2., the rationale being that it makes it easier to find the result based on the number. It seems that 1. is more popular than 2., although 2. still exists, especially in books. I can only imagine that people using 2. must have a reason, but I have not yet to encounter one. I hope it is not too opinion-based to ask:

*What is the rationale for separately numbering theorems, propositions and lemmas, like in 2.?"*

1, maybe I would antepone the number:1-Thm. , 2-Prop., 3-Thm., 4-Lem., etc. $\endgroup$ – Pietro Majer Aug 3 '19 at 8:39