--- a/doc-src/AxClass/Nat/NatClass.thy Mon Jun 26 11:21:49 2000 +0200
+++ b/doc-src/AxClass/Nat/NatClass.thy Mon Jun 26 11:43:56 2000 +0200
@@ -1,7 +1,7 @@
-header {* Defining natural numbers in FOL \label{sec:ex-natclass} *};
+header {* Defining natural numbers in FOL \label{sec:ex-natclass} *}
-theory NatClass = FOL:;
+theory NatClass = FOL:
text {*
\medskip\noindent Axiomatic type classes abstract over exactly one
@@ -12,12 +12,12 @@
We illustrate this with the natural numbers in
Isabelle/FOL.\footnote{See also
\url{http://isabelle.in.tum.de/library/FOL/ex/NatClass.html}}
-*};
+*}
consts
zero :: 'a ("0")
Suc :: "'a \\<Rightarrow> 'a"
- rec :: "'a \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a) \\<Rightarrow> 'a";
+ rec :: "'a \\<Rightarrow> 'a \\<Rightarrow> ('a \\<Rightarrow> 'a \\<Rightarrow> 'a) \\<Rightarrow> 'a"
axclass
nat < "term"
@@ -25,11 +25,11 @@
Suc_inject: "Suc(m) = Suc(n) \\<Longrightarrow> m = n"
Suc_neq_0: "Suc(m) = 0 \\<Longrightarrow> R"
rec_0: "rec(0, a, f) = a"
- rec_Suc: "rec(Suc(m), a, f) = f(m, rec(m, a, f))";
+ rec_Suc: "rec(Suc(m), a, f) = f(m, rec(m, a, f))"
constdefs
add :: "'a::nat \\<Rightarrow> 'a \\<Rightarrow> 'a" (infixl "+" 60)
- "m + n \\<equiv> rec(m, n, \\<lambda>x y. Suc(y))";
+ "m + n \\<equiv> rec(m, n, \\<lambda>x y. Suc(y))"
text {*
This is an abstract version of the plain $Nat$ theory in
@@ -57,6 +57,6 @@
way as for the concrete version. The original proof scripts may be
re-used with some trivial changes only (mostly adding some type
constraints).
-*};
+*}
-end;
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+end
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