A single anchor v can be placed (Fig. 4) either on the internal branch (Case 8) or on a terminal branch (Case 9) of a quartet tree. We prove L<R1=R2 for these: In Case 8, we have: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{array}{*{20}l} {}L = & [\beta -f(e_{1})] \!+ [\beta -f(e_{1})]+[\beta -f(e_{2})]+ [\beta -f(e_{2})] \\ < & 4\beta <[\beta +\alpha e_{1}]+[\beta +\alpha e_{1}] + [\beta +\alpha e_{2}] = R1=R2 \end{array} $$ \end{document}L=[β−f(e1)]+[β−f(e1)]+[β−f(e2)]+[β−f(e2)]<4β<[β+αe1]+[β+αe1]+[β+αe2]=R1=R2