src/HOL/Nat.ML
 changeset 1465 5d7a7e439cec parent 1327 6c29cfab679c child 1475 7f5a4cd08209
```     1.1 --- a/src/HOL/Nat.ML	Tue Jan 30 15:19:20 1996 +0100
1.2 +++ b/src/HOL/Nat.ML	Tue Jan 30 15:24:36 1996 +0100
1.3 @@ -1,6 +1,6 @@
1.4 -(*  Title: 	HOL/nat
1.5 +(*  Title:      HOL/nat
1.6      ID:         \$Id\$
1.7 -    Author: 	Tobias Nipkow, Cambridge University Computer Laboratory
1.8 +    Author:     Tobias Nipkow, Cambridge University Computer Laboratory
1.9      Copyright   1991  University of Cambridge
1.10
1.11  For nat.thy.  Type nat is defined as a set (Nat) over the type ind.
1.12 @@ -47,7 +47,7 @@
1.13  (*Perform induction on n. *)
1.14  fun nat_ind_tac a i =
1.15      EVERY [res_inst_tac [("n",a)] nat_induct i,
1.16 -	   rename_last_tac a ["1"] (i+1)];
1.17 +           rename_last_tac a ["1"] (i+1)];
1.18
1.19  (*A special form of induction for reasoning about m<n and m-n*)
1.20  val prems = goal Nat.thy
1.21 @@ -133,7 +133,7 @@
1.22
1.23  goalw Nat.thy [nat_case_def] "nat_case a f (Suc k) = f(k)";
1.24  by (fast_tac (set_cs addIs [select_equality]
1.25 -	               addEs [make_elim Suc_inject, Suc_neq_Zero]) 1);
1.26 +                       addEs [make_elim Suc_inject, Suc_neq_Zero]) 1);
1.27  qed "nat_case_Suc";
1.28
1.29  (** Introduction rules for 'pred_nat' **)
1.30 @@ -153,7 +153,7 @@
1.31  by (strip_tac 1);
1.32  by (nat_ind_tac "x" 1);
1.33  by (fast_tac (HOL_cs addSEs [mp, pred_natE, Pair_inject,
1.34 -			     make_elim Suc_inject]) 2);
1.35 +                             make_elim Suc_inject]) 2);
1.36  by (fast_tac (HOL_cs addSEs [mp, pred_natE, Pair_inject, Zero_neq_Suc]) 1);
1.37  qed "wf_pred_nat";
1.38
1.39 @@ -245,7 +245,7 @@
1.40  \    |] ==> P";
1.41  by (rtac (major RS tranclE) 1);
1.42  by (REPEAT_FIRST (bound_hyp_subst_tac ORELSE'
1.43 -		  eresolve_tac (prems@[pred_natE, Pair_inject])));
1.44 +                  eresolve_tac (prems@[pred_natE, Pair_inject])));
1.45  by (rtac refl 1);
1.46  qed "lessE";
1.47
1.48 @@ -271,7 +271,7 @@
1.49
1.50  goal Nat.thy "(m < Suc(n)) = (m < n | m = n)";
1.51  by (fast_tac (HOL_cs addSIs [lessI]
1.52 -		     addEs  [less_trans, less_SucE]) 1);
1.53 +                     addEs  [less_trans, less_SucE]) 1);
1.54  qed "less_Suc_eq";
1.55
1.56  val prems = goal Nat.thy "m<n ==> n ~= 0";
1.57 @@ -289,8 +289,8 @@
1.58  by (rtac impI 1);
1.59  by (etac less_zeroE 1);
1.60  by (fast_tac (HOL_cs addSIs [lessI RS less_SucI]
1.62 -		     addEs  [less_trans, lessE]) 1);
1.64 +                     addEs  [less_trans, lessE]) 1);
1.65  qed "Suc_lessD";
1.66
1.67  val [major,minor] = goal Nat.thy
1.68 @@ -315,8 +315,8 @@
1.69  by (rtac impI 1);
1.70  by (etac less_zeroE 1);
1.71  by (fast_tac (HOL_cs addSIs [lessI]