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author | Johannes Kloos <jkloos@mpi-sws.org> | 2017-10-25 22:57:06 +0200 |
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committer | Johannes Kloos <jkloos@mpi-sws.org> | 2017-10-25 22:57:06 +0200 |
commit | 258c6a766d6f5d623925211694e7cede001f872e (patch) | |
tree | b973099fb42803f9544a86540d2f9de9747e7740 /doc | |
parent | 5a7ca0b267e8531137d302b9c54b41bed097085f (diff) |
Rename \Tree to \NatTree
Diffstat (limited to 'doc')
-rw-r--r-- | doc/refman/RefMan-cic.tex | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index 542fdf51e..2695c5eee 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -883,8 +883,8 @@ the type $V$ satisfies the nested positivity condition for $X$ \settowidth\framecharacterwidth{\hh} \newcommand\ws{\hbox{}\hskip\the\framecharacterwidth} \newcommand\ruleref[1]{\hskip.25em\dots\hskip.2em{\em (bullet #1)}} -\newcommand{\Tree}{\mbox{\textsf{nattree}}} -\newcommand{\TreeA}{\mbox{\textsf{nattree}}~\ensuremath{A}} +\newcommand{\NatTree}{\mbox{\textsf{nattree}}} +\newcommand{\NatTreeA}{\mbox{\textsf{nattree}}~\ensuremath{A}} \newcommand{\cnode}{\mbox{\textsf{node}}} \newcommand{\cleaf}{\mbox{\textsf{leaf}}} @@ -897,25 +897,25 @@ Inductive nattree (A:Type) : Type := \end{verbatim} \begin{latexonly} -\noindent Then every instantiated constructor of $\TreeA$ satisfies the nested positivity condition for $\Tree$\\ +\noindent Then every instantiated constructor of $\NatTreeA$ satisfies the nested positivity condition for $\NatTree$\\ \noindent \ws\ws\vv\\ -\ws\ws\vh\hh\ws concerning type $\TreeA$ of constructor $\cleaf$:\\ -\ws\ws\vv\ws\ws\ws\ws Type $\TreeA$ of constructor $\cleaf$ satisfies the positivity condition for $\Tree$\\ -\ws\ws\vv\ws\ws\ws\ws because $\Tree$ does not appear in any (real) arguments of the type of that constructor\\ -\ws\ws\vv\ws\ws\ws\ws (primarily because $\Tree$ does not have any (real) arguments)\ruleref1\\ +\ws\ws\vh\hh\ws concerning type $\NatTreeA$ of constructor $\cleaf$:\\ +\ws\ws\vv\ws\ws\ws\ws Type $\NatTreeA$ of constructor $\cleaf$ satisfies the positivity condition for $\NatTree$\\ +\ws\ws\vv\ws\ws\ws\ws because $\NatTree$ does not appear in any (real) arguments of the type of that constructor\\ +\ws\ws\vv\ws\ws\ws\ws (primarily because $\NatTree$ does not have any (real) arguments)\ruleref1\\ \ws\ws\vv\\ -\ws\ws\hv\hh\ws concerning type $\forall~A\ra(\NN\ra\TreeA)\ra\TreeA$ of constructor $\cnode$:\\ - \ws\ws\ws\ws\ws\ws\ws Type $\forall~A:\Type,A\ra(\NN\ra\TreeA)\ra\TreeA$ of constructor $\cnode$\\ -\ws\ws\ws\ws\ws\ws\ws satisfies the positivity condition for $\Tree$ because:\\ +\ws\ws\hv\hh\ws concerning type $\forall~A\ra(\NN\ra\NatTreeA)\ra\NatTreeA$ of constructor $\cnode$:\\ + \ws\ws\ws\ws\ws\ws\ws Type $\forall~A:\Type,A\ra(\NN\ra\NatTreeA)\ra\NatTreeA$ of constructor $\cnode$\\ +\ws\ws\ws\ws\ws\ws\ws satisfies the positivity condition for $\NatTree$ because:\\ \ws\ws\ws\ws\ws\ws\ws\vv\\ -\ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\Tree$ occurs only strictly positively in $\Type$\ruleref1\\ +\ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\NatTree$ occurs only strictly positively in $\Type$\ruleref1\\ \ws\ws\ws\ws\ws\ws\ws\vv\\ -\ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\Tree$ occurs only strictly positively in $A$\ruleref1\\ +\ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\NatTree$ occurs only strictly positively in $A$\ruleref1\\ \ws\ws\ws\ws\ws\ws\ws\vv\\ - \ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\Tree$ occurs only strictly positively in $\NN\ra\TreeA$\ruleref{3+2}\\ + \ws\ws\ws\ws\ws\ws\ws\vh\hh\ws $\NatTree$ occurs only strictly positively in $\NN\ra\NatTreeA$\ruleref{3+2}\\ \ws\ws\ws\ws\ws\ws\ws\vv\\ -\ws\ws\ws\ws\ws\ws\ws\hv\hh\ws $\Tree$ satisfies the positivity condition for $\TreeA$\ruleref1 +\ws\ws\ws\ws\ws\ws\ws\hv\hh\ws $\NatTree$ satisfies the positivity condition for $\NatTreeA$\ruleref1 \end{latexonly} \begin{rawhtml} <pre> |