\documentclass[../generics]{subfiles}

\begin{document}

\chapter{Derived Requirements Summary}\label{derived summary}

\index{$\vdash$}
\IndexStep{GenSig}
\IndexStep{ReqSig}
\IndexStep{AssocType}
\IndexStep{Conf}
\IndexStep{Equiv}
\IndexStep{Same}
\IndexStep{Member}
\IndexStep{Concrete}

\begin{gather*}
\vdash\ConfReq{T}{P}\tag{\textsc{GenSig}}\\
\vdash\ConfReq{T}{C}\\
\vdash\ConfReq{T}{AnyObject}\\
\vdash\FormalReq{T == U}\\[\medskipamount]
\ConfReq{T}{P}\vdash\texttt{T.A}\tag{\textsc{AssocType}}\\
\ConfReq{T}{P}\vdash\texttt{T.[P]A}\\
\ConfReq{T}{P}\vdash\FormalReq{T.[P]A == T.A}\\[\medskipamount]
\vdash\ConfReq{Self.U}{Q}_\texttt{P}\tag{\textsc{ReqSig}}\\
\vdash\ConfReq{Self.U}{C}_\texttt{P}\\
\vdash\ConfReq{Self.U}{AnyObject}_\texttt{P}\\
\vdash\FormalReq{Self.U == Self.V}_\texttt{P}\\[\medskipamount]
\ConfReq{T}{P},\,\ConfReq{Self.U}{Q}\vdash\ConfReq{T.U}{Q}\tag{\textsc{Conf}}\\
\ConfReq{T}{P},\,\ConfReq{Self.U}{C}\vdash\ConfReq{T.U}{C}\\
\ConfReq{T}{P},\,\ConfReq{Self.U}{AnyObject}\vdash\ConfReq{T.U}{AnyObject}\\
\ConfReq{T}{P},\,\FormalReq{Self.U == Self.V}\vdash\FormalReq{T.U == T.V}\\[\medskipamount]
\texttt{T}\vdash\FormalReq{T == T}\tag{\textsc{Equiv}}\\
\FormalReq{T == U}\vdash\FormalReq{U == T}\\
\FormalReq{T == U},\,\FormalReq{U == V}\vdash\FormalReq{T == V}\\[\medskipamount]
\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\ConfReq{T}{P}\tag{\textsc{Same}}\\
\ConfReq{U}{C},\,\FormalReq{T == U}\vdash\ConfReq{T}{C}\\
\ConfReq{U}{AnyObject},\,\FormalReq{T == U}\vdash\ConfReq{T}{AnyObject}\\[\medskipamount]
\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\FormalReq{T.A == U.A}\tag{\textsc{Member}}\\
\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\FormalReq{T.[P]A == U.[P]A}\\[\medskipamount]
\FormalReq{T == U}\vdash\FormalReq{G<T> == G<U>}\qquad\mbox{(arbitrary type constructor \texttt{G<>})}\tag{\textsc{Concrete}}\\
\FormalReq{G<T> == G<U>}\vdash\FormalReq{T == U}\qquad\mbox{(arbitrary type constructor \texttt{G<>})}
\end{gather*}

\end{document}