I created a world in Minecraft 1.13.1 and want to play that world on Minecraft 1.12.2 without losing my progress?

YOU DON'T!

Whenever you go between major versions (1.xx stuff, like 1.12 & 1.13), more content is added in the game & older worlds can be played with newer versions as the new content will get applied to the world whenever you generate a new chunk (which can potential cause some sudden biome changes between the old chunks & the new chunks). Minor versions (1.xx.y, like 1.13(.0) & 1.13.1) are just bugfixes which doesn't add new content.

HOWEVER, YOU Can't GO BACKWARDS as the old versions won't understand the new content & will cause issues if you try to force it. If the game doesn't crash or have a major error that prevents the world from getting loaded, it will likely have some major gaps in the chunks (where game will likely place an air block or some type of "filler" where the new blocks would be introduced)… Which would make the game world less than desirable.

It MIGHT be possible to convert worlds to older versions with a 3rd party tool (like MCEdit), but it's going to be a massive headache to ensure that EVERY SINGLE WORLD CHUNK IS COMPLIANT WITH THE OLD VERSION to get it to work… Which might not be worth the hassle to do so.

This will leave you with two options.

A) Stick with version 1.13.x & the stuff in it.

B) Start a new world in version 1.12.x (which I know you don't want, but it's the only viable option).

I know it's not the desired answer, but it's the harsh truth that you'll have to live with. I know that there's been a few times I've wanted to do this (back in the alpha / beta phases), but I've come to accept things can only go forward (never backwards).