src/ZF/Nat.ML
changeset 5505 b0856ff6fc69
parent 5479 5a5dfb0f0d7d
child 5529 4a54acae6a15
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5504:739b777e4355 5505:b0856ff6fc69
     1 (*  Title:      ZF/nat.ML
     1 (*  Title:      ZF/nat.ML
     2     ID:         $Id$
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     4     Copyright   1992  University of Cambridge
     5 
     5 
     6 For nat.thy.  Natural numbers in Zermelo-Fraenkel Set Theory 
     6 Natural numbers in Zermelo-Fraenkel Set Theory 
     7 *)
     7 *)
     8 
     8 
     9 open Nat;
     9 open Nat;
    10 
    10 
    11 Goal "bnd_mono(Inf, %X. {0} Un {succ(i). i:X})";
    11 Goal "bnd_mono(Inf, %X. {0} Un {succ(i). i:X})";
   191 qed "succ_lt_induct";
   191 qed "succ_lt_induct";
   192 
   192 
   193 (** nat_case **)
   193 (** nat_case **)
   194 
   194 
   195 Goalw [nat_case_def] "nat_case(a,b,0) = a";
   195 Goalw [nat_case_def] "nat_case(a,b,0) = a";
   196 by (blast_tac (claset() addIs [the_equality]) 1);
   196 by (Blast_tac 1);
   197 qed "nat_case_0";
   197 qed "nat_case_0";
   198 
   198 
   199 Goalw [nat_case_def] "nat_case(a,b,succ(m)) = b(m)";
   199 Goalw [nat_case_def] "nat_case(a,b,succ(m)) = b(m)";
   200 by (blast_tac (claset() addIs [the_equality]) 1);
   200 by (Blast_tac 1);
   201 qed "nat_case_succ";
   201 qed "nat_case_succ";
   202 
   202 
   203 Addsimps [nat_case_0, nat_case_succ];
   203 Addsimps [nat_case_0, nat_case_succ];
   204 
   204 
   205 val major::prems = goal Nat.thy
   205 val major::prems = goal Nat.thy