Sounds a bit silly to write something like that by hand, when you could use BatList.drop_while (from batteries) like so:

    let line_is_not_header line =
        String.length line < 4 || String.sub line 0 3 != "+++"
    match (BatList.drop_while line_is_not_header lines) with
    | header_line :: following_lines ->
        header env header_line;
        modified env 0 following_lines
    | _ -> ()

In practice, I find that it's rarely useful to write recursive functions by hand, unless you're willing to limit yourself to the default stdlib.