Let ... then ... in mathematical definition

I am writing mathematical definitions in my scientific publications. My editor corrected the definitions in two different ways, but not consistently.

The editor is not from a publisher. It is a service that checks my punctuation and spelling, before I submit my paper for peer-review.

Now, I am not sure which version is correct:

Version 1:

Let A, and B; then, C.

Version 2:

Let A, and B. Then, C.

Version 3:

Let A, and B; then C.

Version 4:

Let A, and B, then C.

Edit: After reading

• https://www.grammarly.com/blog/semicolon/ seems to suggest that version 1 is correct.
• https://www.impan.pl/wydawnictwa/dla-autorow/errors.pdf suggests that version 2 is correct and version 4 is wrong.
• https://www.margieholdscourt.com/the-word-then-2/ seems to suggests that version 3 is correct.
• Is it true you should never put a comma after "then"? Please explain seems to suggest that version 3 is correct.
• https://linguaholic.com/linguablog/comma-before-then/ seems to suggests that version 4 is correct.
• https://faculty.math.illinois.edu/~west/grammar.html#letthen suggests that version 4 is correct and version 2 is wrong.

Additionally I read

• Semi-colon or comma before then?
• http://www.sussex.ac.uk/informatics/punctuation/colonandsemi/semi

In any case, I am none the wiser.

This is a definition? That is: A,B is the setting and C is the actual definition? If so: Definitely no comma after "then". Probably a period after B (although semicolon or comma are OK). If there are only two items A,B with "and" between, then no comma is needed.

Let n be a positive integer and let A be an n x n matrix. Then A is said to be singular iff ...