% relational operators
\def\lele#1#2#3{\ensuremath{{#1}\leq{#2}\leq{#3}}}
\def\ltlt#1#2#3{\ensuremath{{#1}<{#2}<{#3}}}
\def\lelt#1#2#3{\ensuremath{{#1}\leq{#2}<{#3}}}
\def\ltle#1#2#3{\ensuremath{{#1}<{#2}\leq{#3}}}

% quantifier
\def\bnd#1#2#3#4{\ensuremath{{#1}{#2}:{#3}:{#4}}}
\def\bndsum#1#2#3{\bnd{\sum}{#1}{#2}{#3}}


% numbers
\def\Nat{\ensuremath{\mathbb{N}}}
\def\Int{\ensuremath{\mathbb{Z}}}

% propositional constants
\def\cand{\ensuremath{\text{\bf\mbox{ cand }}}}
\def\land{\ensuremath{\wedge}}
\def\lor{\ensuremath{\vee}}
\def\limp{\ensuremath{\Rightarrow}}
\def\lequiv{\ensuremath{\equiv}}

% proof steps
\def\justify#1{\langle{#1}\rangle}
