The new content doesn't "slide in". What you are doing is shifting the entire screen up. What you need to do is hide the top and bottom borders.
Then you need to scroll the screen up. Once you've scrolled 8 pixel lines, what you need to do, is reset the scroll and then at the same time COPY the characters on the screen up a row, and add the new row at the bottom.
Then continue to smooth scroll up.

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