src/HOLCF/Cprod1.ML
author nipkow
Thu Oct 12 18:38:23 2000 +0200 (2000-10-12)
changeset 10212 33fe2d701ddd
parent 9248 e1dee89de037
child 11025 a70b796d9af8
permissions -rw-r--r--
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     1 (*  Title:      HOLCF/Cprod1.ML
     2     ID:         $Id$
     3     Author:     Franz Regensburger
     4     Copyright   1993  Technische Universitaet Muenchen
     5 
     6 Partial ordering for cartesian product of HOL theory Product_Type.thy
     7 *)
     8 
     9 
    10 (* ------------------------------------------------------------------------ *)
    11 (* less_cprod is a partial order on 'a * 'b                                 *)
    12 (* ------------------------------------------------------------------------ *)
    13 
    14 Goal "[|fst x = fst y; snd x = snd y|] ==> x = y";
    15 by (subgoal_tac "(fst x,snd x)=(fst y,snd y)" 1);
    16 by (rotate_tac ~1 1);
    17 by (asm_full_simp_tac(HOL_ss addsimps[surjective_pairing RS sym])1);
    18 by (asm_simp_tac (simpset_of Product_Type.thy) 1);
    19 qed "Sel_injective_cprod";
    20 
    21 Goalw [less_cprod_def] "(p::'a*'b) << p";
    22 by (Simp_tac 1);
    23 qed "refl_less_cprod";
    24 
    25 Goalw [less_cprod_def] "[|(p1::'a * 'b) << p2;p2 << p1|] ==> p1=p2";
    26 by (rtac Sel_injective_cprod 1);
    27 by (fast_tac (HOL_cs addIs [antisym_less]) 1);
    28 by (fast_tac (HOL_cs addIs [antisym_less]) 1);
    29 qed "antisym_less_cprod";
    30 
    31 Goalw [less_cprod_def]
    32         "[|(p1::'a*'b) << p2;p2 << p3|] ==> p1 << p3";
    33 by (rtac conjI 1);
    34 by (fast_tac (HOL_cs addIs [trans_less]) 1);
    35 by (fast_tac (HOL_cs addIs [trans_less]) 1);
    36 qed "trans_less_cprod";