\newcommand{\onety}{\mathbf{1}}
\newcommand{\zeroty}{\mathbf{0}}
\newcommand{\twoty}{\mathbf{2}}
\newcommand{\ansty}{\twoty}
\newcommand{\prodty}[2]{{#1}\times{#2}}
\newcommand{\sumty}[2]{{#1}+{#2}}
\newcommand{\funty}[2]{{#1}\to{#2}}
\newcommand{\allty}[2]{\forall{#1}{.}{#2}}
\newcommand{\somety}[2]{\exists{#1}{.}{#2}}
\newcommand{\natty}{\ensuremath{\mathbf{\mathsf{N}}}}
\newcommand{\conatty}{\reflectbox{\ensuremath{\mathbf{\mathsf{N}}}}}

\newcommand{\yesex}{\mathbf{\mathsf{Y}}}
\newcommand{\noex}{\mathbf{\mathsf{N}}}
\newcommand{\unitex}{\mathbf{\mathsf{\star}}}
\newcommand{\pairex}[2]{\langle {#1}\mathbin{,} {#2}\rangle}
\newcommand{\lftex}[1]{{#1}\cdot {\mathbf{\mathsf{1}}}}
\newcommand{\rhtex}[1]{{#1}\cdot\mathbf{\mathsf{2}}}
\newcommand{\inlex}[1]{\mathbf{\mathsf{1}}\cdot{#1}}
\newcommand{\caseex}[6]{\mathbf{\mathsf{case}}_{#1}(#2;#3{.}#4;#5{.}#6)}
\newcommand{\inrex}[1]{\mathbf{\mathsf{2}}\cdot{#1}}
\newcommand{\lamex}[3]{\lambda_{#1}({#2}\mathbin{.}{#3})}
\newcommand{\ulamex}[2]{\lambda {#1}{.}{#2}}
\newcommand{\appex}[2]{\mathbf{\mathsf{ap}}(#1,#2)}
\newcommand{\Lamex}[2]{\Lambda {#1}{.}{#2}}
\newcommand{\uLamex}[1]{\Lambda{.}{#1}}
\newcommand{\Appex}[2]{\mathbf{\mathsf{Ap}}(#1,#2)}
\newcommand{\uAppex}[1]{\mathbf{\mathsf{Ap}}{(#1)}}
\newcommand{\packex}[2]{\mathbf{\mathsf{pack}}[#1](#2)}
\newcommand{\openex}[5]{\mathbf{\mathsf{open}}[#1](#2;#3{.}#4{.}#5)}
\newcommand{\zeroex}{\textsf{zero}}
\newcommand{\succex}[1]{\textsf{succ}(#1)}
\newcommand{\recex}[5]{\textsf{rec}_{#1}(#2;#3;#4{.}#5)}
\newcommand{\predex}[1]{\textsf{pred}(#1)}
\newcommand{\genex}[4]{\textsf{gen}_{#1}(#2;#3{.}#4)}

\newcommand{\betared}{\mathrel{\rightarrow_\beta}}
\newcommand{\betastar}{\mathrel{\rightarrow^\ast_\beta}}
\newcommand{\betaplus}{\mathrel{\rightarrow^{+}_\beta}}
\newcommand{\betanorm}[1]{\textsf{norm}_\beta(#1)}
\newcommand{\betahd}{\mathrel{\mapsto_\beta}}
