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authorMatej Kosik2015-11-02 16:58:39 +0100
committerHugo Herbelin2015-12-10 09:35:11 +0100
commitfdb02e793da45a37355050342109da1be4a49c89 (patch)
treefdb7461ca8e1c1961159fee40e9de75f69a82b1a /doc
parent10f9c82c38c6eb01e64ab9a8fa233300568c18d4 (diff)
TYPOGRAPHY: Examples of "arity" concept(s) were put to a separate \paragraph{...}
Diffstat (limited to 'doc')
-rw-r--r--doc/refman/RefMan-cic.tex23
1 files changed, 15 insertions, 8 deletions
diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex
index deaa1047c8..2fa9c59a86 100644
--- a/doc/refman/RefMan-cic.tex
+++ b/doc/refman/RefMan-cic.tex
@@ -766,16 +766,23 @@ We restrict ourselves to definitions which
satisfy a syntactic criterion of positivity. Before giving the formal
rules, we need a few definitions:
-\paragraph[Definitions]{Definitions\index{Positivity}\label{Positivity}}
-
-A type $T$ is an {\em arity of sort $s$}\index{Arity} if it converts
+\paragraph[Definition]{Definition\index{Arity}\label{Arity}}
+A type $T$ is an {\em arity of sort $s$} if it converts
to the sort $s$ or to a product $\forall~x:T,U$ with $U$ an arity
-of sort $s$. (For instance $A\ra \Set$ or $\forall~A:\Prop,A\ra
-\Prop$ are arities of sort respectively \Set\ and \Prop).
-\vskip.5em
-\noindent A type $T$ is an {\em arity} if there is a $s\in\Sort$
+of sort $s$.
+
+\paragraph[Examples]{Examples}
+$A\ra \Set$ is an arity of sort $\Set$.
+$\forall~A:\Prop,A\ra \Prop$ is an arity of sort \Prop.
+
+\paragraph[Definition]{Definition}
+A type $T$ is an {\em arity} if there is a $s\in\Sort$
such that $T$ is an arity of sort $s$.
-\vskip.5em
+
+\paragraph[Examples]{Examples}
+$A\ra \Set$ and $\forall~A:\Prop,A\ra \Prop$ are arities.
+
+\paragraph[Definition]{Definition\index{Positivity}\label{Positivity}}
\noindent A {\em type
of constructor of $I$}\index{Type of constructor} is either a term
$(I~t_1\ldots ~t_n)$ or $\fa x:T,C$ with $C$ recursively