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| author | barras | 2003-12-19 17:48:34 +0000 |
|---|---|---|
| committer | barras | 2003-12-19 17:48:34 +0000 |
| commit | c1e8b8c5cbc0e19703b9b7326401e242cd751b80 (patch) | |
| tree | 1d09fa39c291fa810158a5e46d44a000c96f5296 /doc/RefMan-lib.tex | |
| parent | bef467cfac0b718bffdbb5444b2a4364b3941b09 (diff) | |
*** empty log message ***
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8424 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'doc/RefMan-lib.tex')
| -rwxr-xr-x | doc/RefMan-lib.tex | 18 |
1 files changed, 10 insertions, 8 deletions
diff --git a/doc/RefMan-lib.tex b/doc/RefMan-lib.tex index 0d87023155..a8aefe781d 100755 --- a/doc/RefMan-lib.tex +++ b/doc/RefMan-lib.tex @@ -141,10 +141,10 @@ First, we find propositional calculus connectives: \begin{coq_eval} Set Printing Depth 50. -\end{coq_eval} -\begin{coq_example*} (********** Next parsing errors for /\ and \/ are harmless ***********) (******************* since output is not displayed *******************) +\end{coq_eval} +\begin{coq_example*} Inductive True : Prop := I. Inductive False : Prop := . Definition not (A: Prop) := A -> False. @@ -161,14 +161,14 @@ Abort All. \ttindex{or\_introl} \ttindex{or\_intror} \ttindex{iff} -\ttindex{IF} +\ttindex{IF_then_else} \begin{coq_example*} End Projections. Inductive or (A B:Prop) : Prop := | or_introl (_:A) | or_intror (_:B). Definition iff (P Q:Prop) := (P -> Q) /\ (Q -> P). -Definition IF (P Q R:Prop) := P /\ Q \/ ~ P /\ R. +Definition IF_then_else (P Q R:Prop) := P /\ Q \/ ~ P /\ R. \end{coq_example*} \subsubsection{Quantifiers} \label{Quantifiers} @@ -188,7 +188,7 @@ Definition all (A:Set) (P:A -> Prop) := forall x:A, P x. Inductive ex (A: Set) (P:A -> Prop) : Prop := ex_intro (x:A) (_:P x). Inductive ex2 (A:Set) (P Q:A -> Prop) : Prop := - ex_intro2 : (x:A) (_:P x) (_:Q x). + ex_intro2 (x:A) (_:P x) (_:Q x). \end{coq_example*} The following abbreviations are allowed: @@ -389,7 +389,7 @@ provided. \begin{coq_example*} Inductive sig (A:Set) (P:A -> Prop) : Set := exist (x:A) (_:P x). Inductive sig2 (A:Set) (P Q:A -> Prop) : Set := - exist2 : (x:A) (_:P x) (_:Q x). + exist2 (x:A) (_:P x) (_:Q x). \end{coq_example*} A ``strong (dependent) sum'' \verb+{x:A & (P x)}+ may be also defined, @@ -412,10 +412,12 @@ Variable A : Set. Variable P : A -> Set. Definition projS1 (H:sigS A P) := let (x, h) := H in x. Definition projS2 (H:sigS A P) := - let (x, h) return P (projS1 H) := H in h. + match H return P (projS1 H) with + existS x h => h + end. End sigSprojections. Inductive sigS2 (A: Set) (P Q:A -> Set) : Set := - existS2 : (x:A) (_:P x) (_:Q x). + existS2 (x:A) (_:P x) (_:Q x). \end{coq_example*} A related non-dependent construct is the constructive sum |
