Ahoy there
po1040, I missed your post, sorry or I didn't get at first as to what you were about
root 4 has nothing besides a few pokemon, so just exit it to the other end's cerulian city, which has the second gym not the third by the way
Once you've defeated her. go north of the city take the north exit is what I mean,and you'll get your rival who appears out of nowhere to chalange you if I remember right that is
Then you'll have to take on 5 trainers on the bridge defeat them all and you'll get a Nugget, its useless as far as I know so you can sell It for around 5k
go east and so on,until you reach bills house,do what he tells you to do, that is just talk with his computer and you'll have a ticket to board the S.S.ANNE which you can find in Vermilion City.
Head back to cerulean, go to a house where a robbery has taken place, go to the backyard,fight the rockit and you'll get a nice tm, dig
go right from there as much as you can,then start heading south to root5, cross it go underground path, and exit in root6
which connects to Vermilion City. defeat everyone in the S.S.Anne, talk to the captain to gain the hm01 (cut)
You can get to the third gym now,as you have cut and that gym was blocked off to you because it was blocked by a tree. so use your hm01 cut on the tree, enter the gym and defeat your man
A walkthrough would've explained all this a lot better,though. 
grryf
Of all sad words of tongue or pen, the saddest are these, ‘It might have been.
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