bussproofs & trees

1 files changed, 7 insertions, 1 deletions

diff --git a/preamble.tex b/preamble.tex
index 3aeecda..84f87fc 100644
--- a/preamble.tex
+++ b/preamble.tex
@@ -1,6 +1,9 @@
 \usepackage{listings}
 \usepackage{algorithmic}
 \usepackage{amsmath}
+\usepackage{bussproofs}
+\usepackage{tikz}
+\usepackage{tikz-qtree,tikz-qtree-compat}
 
 \renewcommand{\algorithmicrequire}{\textbf{Input:}}
 \renewcommand{\algorithmicensure}{\textbf{Output:}}
@@ -17,4 +20,7 @@ postbreak=\raisebox{0ex}[0ex][0ex]{\ensuremath{\color{red}\hookrightarrow\space}
 %\DeclareMathOperator{\P}{\frak{P}}
 %\DeclareMathOperator{\exp}{exp}
 %\DeclareMathOperator{\ln}{ln}
-\newcommand{\N}{\ensuremath{\mathbb{N}}}
+\providecommand{\N}{\ensuremath{\mathbb{N}}}
+\providecommand{\lequiv}{\ensuremath{\Leftrightarrow}}
+\providecommand{\limplies}{\ensuremath{\Rightarrow}}
+\providecommand{\seq}{\ensuremath{\Longrightarrow}}