Skip to content

Commit

Permalink
Minor corrections
Browse files Browse the repository at this point in the history
  • Loading branch information
Casteran committed Jan 24, 2024
1 parent 14bf0de commit af30acc
Show file tree
Hide file tree
Showing 2 changed files with 6 additions and 5 deletions.
4 changes: 2 additions & 2 deletions doc/ordinal-chapter.tex
Original file line number Diff line number Diff line change
Expand Up @@ -924,7 +924,7 @@ \subsubsection{Building an instance of \texttt{ON}}
There is no interesting arithmetic on finite ordinals, since functions like successor, addition, etc., cannot be represented in \coq{} as \emph{total} functions.
\end{remark}

\section{See also \dots}
\subsubsection{See also \dots}

\gaiasign Finite ordinals are also formalized in \ssreflect/\mathcomp~\cite{MCB}. In Module~\href{../theories/html/gaia_hydras.ON_gfinite.html}{gaia\_hydras.ON\_gfinite}, we build an instance of class \texttt{ON}.

Expand All @@ -936,7 +936,7 @@ \section{See also \dots}



See also Adam Chlipala's \emph{CPDT}~\cite{chlipalacpdt2011} for a thorough study of the use of dependent types.




Expand Down
7 changes: 4 additions & 3 deletions theories/ordinals/OrdinalNotations/ON_Generic.v
Original file line number Diff line number Diff line change
Expand Up @@ -24,8 +24,9 @@ Delimit Scope ON_scope with on.
Class ON {A:Type} (lt: relation A) (cmp: Compare A) :=
{
ON_comp :> Comparable lt cmp;
ON_wf :> well_founded lt;
ON_wf : well_founded lt;
}.

#[global] Existing Instance ON_comp.
Coercion ON_wf : ON >-> well_founded.

Expand Down Expand Up @@ -94,8 +95,8 @@ Class SubON
{
SubON_compare: forall x y : A,
compareB (iota x) (iota y) = compareA x y;
SubON_incl : forall x, ltB (iota x) alpha;
SubON_onto : forall y, ltB y alpha -> exists x:A, iota x = y}.
SubON_incl : forall x, ltB (iota x) alpha;
SubON_onto : forall y, ltB y alpha -> exists x:A, iota x = y}.

(* end snippet SubONDef *)

Expand Down

0 comments on commit af30acc

Please sign in to comment.