# HG changeset patch # User paulson # Date 933094720 -7200 # Node ID cfc11af6174a5c147b61fd8c953f3ac2e0799248 # Parent 6f18ae72a90e66140e9541e188b631a90e15b761 fixed the comments... diff -r 6f18ae72a90e -r cfc11af6174a src/Sequents/LK/Nat.ML --- 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]; diff -r 6f18ae72a90e -r cfc11af6174a src/Sequents/LK/Nat.thy --- 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"