fixed the comments...
--- a/src/Sequents/LK/Nat.ML Tue Jul 27 18:52:48 1999 +0200
+++ b/src/Sequents/LK/Nat.ML Tue Jul 27 18:58:40 1999 +0200
@@ -1,9 +1,9 @@
-(* Title: FOL/ex/Nat.ML
+(* Title: Sequents/LK/Nat
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1992 University of Cambridge
+ Copyright 1999 University of Cambridge
-Proofs about the natural numbers.
+Theory of the natural numbers: Peano's axioms, primitive recursion
*)
Addsimps [Suc_neq_0];
--- a/src/Sequents/LK/Nat.thy Tue Jul 27 18:52:48 1999 +0200
+++ b/src/Sequents/LK/Nat.thy Tue Jul 27 18:58:40 1999 +0200
@@ -1,9 +1,7 @@
-(* Title: FOL/ex/Nat.thy
+(* Title: Sequents/LK/Nat
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1992 University of Cambridge
-
-Examples for the manuals.
+ Copyright 1999 University of Cambridge
Theory of the natural numbers: Peano's axioms, primitive recursion
*)
@@ -17,8 +15,9 @@
"+" :: [nat, nat] => nat (infixl 60)
rules
- induct "[| $H |- $E, P(0), $F;
- !!x. $H |- $E, P(x) --> P(Suc(x)), $F |] ==> $H |- $E, P(n), $F"
+ induct "[| $H |- $E, P(0), $F;
+ !!x. $H |- $E, P(x) --> P(Suc(x)), $F |] ==> $H |- $E, P(n), $F"
+
Suc_inject "|- Suc(m)=Suc(n) --> m=n"
Suc_neq_0 "|- Suc(m) ~= 0"
rec_0 "|- rec(0,a,f) = a"