Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{a,b,c,d\}\subset \mathcal {L}$\end{document}{a,b,c,d}⊂ℒ be four arbitrary leaves and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {L}^{\prime }=\mathcal {L}- \{a,b,c,d\}$\end{document}ℒ′=ℒ−{a,b,c,d}. W.l.o.g assume \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ab.cd \in \mathcal {Q}^{T}$\end{document}ab.cd∈QT. We prove that the four point conditions hold for this arbitrarily chosen quartet in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{\prime }_{uv},D^{\prime }_{v},$\end{document}Duv′,Dv′, and D ′; we also prove that the four point conditions are true for a tree compatible with the tree T. Proving these conditions for arbitrary quartets completes the proof by results of Buneman .