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| -rw-r--r-- | doc/common/macros.tex | 5 | ||||
| -rw-r--r-- | doc/refman/RefMan-cic.tex | 36 |
2 files changed, 41 insertions, 0 deletions
diff --git a/doc/common/macros.tex b/doc/common/macros.tex index 1ac29b155..0ea2ed650 100644 --- a/doc/common/macros.tex +++ b/doc/common/macros.tex @@ -280,6 +280,11 @@ \newcommand{\Type}{\mbox{\textsf{Type}}} \newcommand{\unfold}{\mbox{\textsf{unfold}}} \newcommand{\zeros}{\mbox{\textsf{zeros}}} +\newcommand{\even}{\mbox{\textsf{even}}} +\newcommand{\odd}{\mbox{\textsf{even}}} +\newcommand{\evenO}{\mbox{\textsf{even\_O}}} +\newcommand{\evenS}{\mbox{\textsf{even\_S}}} +\newcommand{\oddS}{\mbox{\textsf{odd\_S}}} %%%%%%%%% % Misc. % diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index bbf637284..101c4e503 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -642,6 +642,42 @@ and thus it enriches the global environment with the following entry: \noindent If we take the following inductive definition: \begin{coq_example*} +Inductive even : nat -> Prop := + | even_O : even 0 + | even_S : forall n, odd n -> even (S n) +with odd : nat -> Prop := + | odd_S : forall n, even n -> odd (S n). +\end{coq_example*} +then: +\def\GammaI{\left[\begin{array}{r \colon l} + \even & \nat\ra\Prop \\ + \odd & \nat\ra\Prop + \end{array} + \right]} +\def\GammaC{\left[\begin{array}{r \colon l} + \evenO & \even~\nO \\ + \evenS & \forall n : \nat, \odd~n \ra \even~(\nS~n) + \end{array} + \right]} +\begin{itemize} + \item $p = 1$ + \item $\Gamma_I = \GammaI$ + \item $\Gamma_C = \GammaC$ +\end{itemize} +and thus it enriches the global environment with the following entry: +\vskip.5em +\ind{p}{\Gamma_I}{\Gamma_C} +\vskip.5em +\noindent that is: +\vskip.5em +\ind{1}{\GammaI}{\GammaC} +\vskip.5em +\noindent In this case, $\Gamma_P=[A:\Type]$. + +\vskip1em\hrule\vskip1em + +\noindent If we take the following inductive definition: +\begin{coq_example*} Inductive has_length (A : Type) : list A -> nat -> Prop := | nil_hl : has_length A (nil A) O | cons_hl : forall (a:A) (l:list A) (n:nat), |