Working with multiple branches

There is a branch on a remote but this branch does not exist locally, and I want it locally:

git fetch $remote_name
git branch $local_branch_name $remote_name/$remote_branch_name

There is a local branch which does not exist on the remote, and I want it on the remote:

git checkout $local_branch_name
git push [-u] $remote_name $remote_branch_name

I have been working on a feature branch, but the main branch has advanced in the meantime. I want to rebase so that my feature branch has the changes made in the main (remember that rebasing changes the history!):

git checkout $feature_branch
git rebase $main_branch