diff --git a/paper-new/defs.tex b/paper-new/defs.tex
index 864e38d1dbcc246c87494ffabcdaf57ee7bc7aac..31c50e23d34cb49f81bd1e1e3860194578c89696 100644
--- a/paper-new/defs.tex
+++ b/paper-new/defs.tex
@@ -3,6 +3,8 @@
 \newcommand{\inr}{\mathsf{inr}}
 \newcommand{\alt}{\mathrel{\bf \,\mid\,}}
 
+\newcommand{\ob}{\text{Ob}}
+
 
 \newcommand{\extlc}{\text{Ext-}\lambda}
 \newcommand{\extlcm}{\text{Ext-}\lambda^{-\text{trans}}}
@@ -57,6 +59,7 @@
 
 %\newcommand{\rel}{\circ\hspace{-4px}-\hspace{-4px}\bullet}
 \newcommand{\rel}{\mathrel{\circ\mkern-6mu-\mkern-6mu\bullet}}
+\newcommand{\wand}{\mathrel{-\mkern-6mu*}}
 \newcommand{\ltdyn}{\sqsubseteq}
 \newcommand{\gtdyn}{\sqsupseteq}
 \newcommand{\equidyn}{\mathrel{\gtdyn\ltdyn}}
@@ -155,5 +158,44 @@
 \newcommand{\push}{\text{push}}
 \newcommand{\pull}{\text{pull}}
 
+\newcommand{\pv}{P^{\mathcal{V}}}
+\newcommand{\pe}{P^{\mathcal{E}}}
+\newcommand{\ptbv}{\text{ptb}^\mathcal{V}}
+\newcommand{\ptbe}{\text{ptb}^\mathcal{E}}
+
 \newcommand{\upf}{\text{up}}
-\newcommand{\dnf}{\text{dn}}
\ No newline at end of file
+\newcommand{\dnf}{\text{dn}
+}
+\newcommand{\arr}{\to}
+\newcommand{\comp}{\bullet}
+
+\newcommand{\vf}{\mathcal{V}_f}
+\newcommand{\vsq}{\mathcal{V}_{sq}}
+\newcommand{\ef}{\mathcal{E}_f}
+\newcommand{\esq}{\mathcal{E}_{sq}}
+
+\newcommand{\sv}{s_{\mathcal{V}}}
+\newcommand{\tv}{t_{\mathcal{V}}}
+\newcommand{\rv}{r_{\mathcal{V}}}
+\newcommand{\se}{s_{\mathcal{E}}}
+\newcommand{\te}{t_{\mathcal{E}}}
+\newcommand{\re}{r_{\mathcal{E}}}
+
+\newcommand{\Ff}{F_f}
+\newcommand{\Fsq}{F_{sq}}
+\newcommand{\Uf}{U_f}
+\newcommand{\Usq}{U_{sq}}
+
+\newcommand{\vsim}{\mathcal{V}_{\bisim}}
+\newcommand{\esim}{\mathcal{E}_{\bisim}}
+\newcommand{\svsim}{s_{\mathcal{V}}^\bisim}
+\newcommand{\tvsim}{t_{\mathcal{V}}^\bisim}
+\newcommand{\rvsim}{r_{\mathcal{V}}^\bisim}
+\newcommand{\sesim}{s_{\mathcal{E}}^\bisim}
+\newcommand{\tesim}{t_{\mathcal{E}}^\bisim}
+\newcommand{\resim}{r_{\mathcal{E}}^\bisim}
+
+
+
+\newcommand{\ve}{\mathcal{V}_e}
+\newcommand{\ee}{\mathcal{E}_e} 
\ No newline at end of file