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1 (* Title: HOL/Lex/Prefix.thy |
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2 ID: $Id$ |
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3 Author: Richard Mayr & Tobias Nipkow |
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4 Copyright 1995 TUM |
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5 *) |
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6 |
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7 open Prefix; |
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8 |
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9 val [maj,min] = goal Prefix.thy "[| Q([]); !! y ys. Q(y#ys) |] ==> ! l.Q(l)"; |
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10 br allI 1; |
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11 by (list.induct_tac "l" 1); |
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12 br maj 1; |
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13 br min 1; |
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14 val list_cases = result(); |
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15 |
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16 goalw Prefix.thy [prefix_def] "[] <= xs"; |
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17 by (simp_tac (!simpset addsimps [eq_sym_conv]) 1); |
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18 qed "Nil_prefix"; |
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19 Addsimps[Nil_prefix]; |
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20 |
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21 goalw Prefix.thy [prefix_def] "(xs <= []) = (xs = [])"; |
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22 by (list.induct_tac "xs" 1); |
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23 by (Simp_tac 1); |
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24 by (fast_tac HOL_cs 1); |
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25 by (Simp_tac 1); |
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26 qed "prefix_Nil"; |
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27 Addsimps [prefix_Nil]; |
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28 |
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29 (* nicht sehr elegant bewiesen - Induktion eigentlich ueberfluessig *) |
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30 goalw Prefix.thy [prefix_def] |
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31 "(xs <= y#ys) = (xs=[] | (? zs. xs=y#zs & zs <= ys))"; |
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32 by (list.induct_tac "xs" 1); |
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33 by (Simp_tac 1); |
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34 by (fast_tac HOL_cs 1); |
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35 by (Simp_tac 1); |
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36 by (fast_tac HOL_cs 1); |
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37 qed "prefix_Cons"; |
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38 |
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39 goalw Prefix.thy [prefix_def] "(x#xs <= y#ys) = (x=y & xs<=ys)"; |
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40 by(Simp_tac 1); |
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41 by (fast_tac HOL_cs 1); |
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42 qed"Cons_prefix_Cons"; |
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43 Addsimps [Cons_prefix_Cons]; |