src/HOLCF/Sprod1.ML
author wenzelm
Thu Aug 27 20:46:36 1998 +0200 (1998-08-27)
changeset 5400 645f46a24c72
parent 3323 194ae2e0c193
child 9245 428385c4bc50
permissions -rw-r--r--
made tutorial first;
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(*  Title:      HOLCF/Sprod1.ML
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    ID:         $Id$
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    Author:     Franz Regensburger
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    Copyright   1993  Technische Universitaet Muenchen
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Lemmas for theory Sprod1.thy
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*)
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open Sprod1;
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(* ------------------------------------------------------------------------ *)
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(* less_sprod is a partial order on Sprod                                   *)
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(* ------------------------------------------------------------------------ *)
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qed_goalw "refl_less_sprod" thy [less_sprod_def]"(p::'a ** 'b) << p"
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(fn prems => [(fast_tac (HOL_cs addIs [refl_less]) 1)]);
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qed_goalw "antisym_less_sprod" thy [less_sprod_def]
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        "[|(p1::'a ** 'b) << p2;p2 << p1|] ==> p1=p2"
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(fn prems =>
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        [
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        (cut_facts_tac prems 1),
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        (rtac Sel_injective_Sprod 1),
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        (fast_tac (HOL_cs addIs [antisym_less]) 1),
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        (fast_tac (HOL_cs addIs [antisym_less]) 1)
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        ]);
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qed_goalw "trans_less_sprod" thy [less_sprod_def]
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        "[|(p1::'a**'b) << p2;p2 << p3|] ==> p1 << p3"
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(fn prems =>
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        [
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        (cut_facts_tac prems 1),
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        (rtac conjI 1),
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        (fast_tac (HOL_cs addIs [trans_less]) 1),
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        (fast_tac (HOL_cs addIs [trans_less]) 1)
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        ]);