diff --git a/tex/paper.mng b/tex/paper.mng index abf81075..1814d3d0 100644 --- a/tex/paper.mng +++ b/tex/paper.mng @@ -43,6 +43,8 @@ \newcommand{\eqrefl}{\text{eq-refl~}} \newcommand{\secondDP}{\text{second-dp~}} +\newcommand\prooftermname[1]{\texttt{#1}} + \begin{document} \newNTclass{nonterm} @@ -303,7 +305,7 @@ We prove some of the usual metatheoretical properties of the proposed language. We also provide machine-verified proofs of these theorems in the supplemental code, with the corresponding proof terms referred in lemmas statements. -\begin{lemma}[Agreement I, \verb +T-implies-TCTX]\label{lma:term_wf_implies_ctx_wf} +\begin{lemma}[Agreement I, \prooftermname{T-implies-TCTX}]\label{lma:term_wf_implies_ctx_wf} If $[[ G |- es : ts ]]$, then $[[ G ok ]]$. \end{lemma} \begin{proof} @@ -312,7 +314,7 @@ with the corresponding proof terms referred in lemmas statements. and the other rules recurse on one of their premises. \end{proof} -\begin{lemma}[Agreement II, \verb +TWF-implies-TCTX]\label{lma:type_wf_implies_ctx_wf} +\begin{lemma}[Agreement II, \prooftermname{TWF-implies-TCTX}]\label{lma:type_wf_implies_ctx_wf} If $[[ G |- ts ]]$, then $[[G ok]]$. \end{lemma} \begin{proof} @@ -325,10 +327,10 @@ with the corresponding proof terms referred in lemmas statements. For the following two lemmas, assume $[[ G ]]$, $[[ G' ]]$ are contexts such that $[[ G ]] \subset [[ G' ]]$ and $[[ G' ok ]]$. Then: -\begin{lemma}[Thinning on types, \verb +twf-thinning]\label{lma:thinning_twf} +\begin{lemma}[Thinning on types, \prooftermname{twf-thinning}]\label{lma:thinning_twf} If $[[ G |- ts ]]$, then $[[ G' |- ts ]]$. \end{lemma} -\begin{lemma}[Thinning on terms, \verb +t-thinning]\label{lma:thinning_t} +\begin{lemma}[Thinning on terms, \prooftermname{t-thinning}]\label{lma:thinning_t} If $[[ G |- es : ts ]]$, then $[[ G' |- es : ts ]]$. \end{lemma} These two lemmas are proven using mutual induction, @@ -352,7 +354,7 @@ this is a well-founded proof. then it must conclude $[[ [| G' |] => A v. (r1 => r2) ]]$. \end{proof} -\begin{lemma}[Substitution on types, \verb +sub-TWF]\label{lma:type_substitution} +\begin{lemma}[Substitution on types, \prooftermname{sub-TWF}]\label{lma:type_substitution} Assume $[[ G, x : ts, GD |- ts' ]]$ and $[[ G |- es : ts ]]$, then $[[ G, [ x |-> es ] GD |- [ x |-> es ] ts' ]] $. \end{lemma} \begin{proof} @@ -361,7 +363,7 @@ this is a well-founded proof. We refer the interested reader to the formal proof of theorem in the supplemental code for the specific details. \end{proof} -\begin{lemma}[Agreement III, \verb +T-implies-TWF]\label{lma:term_wf_implies_type_wf} +\begin{lemma}[Agreement III, \prooftermname{T-implies-TWF}]\label{lma:term_wf_implies_type_wf} If $[[ G |- es : ts ]]$, then $[[ G |- ts ]]$. \end{lemma} \begin{proof}