src/HOL/AxClasses/Lattice/LatPreInsts.ML
author wenzelm
Mon Nov 03 12:24:13 1997 +0100 (1997-11-03)
changeset 4091 771b1f6422a8
parent 1899 0075a8d26a80
child 4153 e534c4c32d54
permissions -rw-r--r--
isatool fixclasimp;
     1 
     2 open LatPreInsts;
     3 
     4 
     5 (** complete lattices **)
     6 
     7 goal thy "is_inf x y (Inf {x, y})";
     8   br (bin_is_Inf_eq RS subst) 1;
     9   br Inf_is_Inf 1;
    10 qed "Inf_is_inf";
    11 
    12 goal thy "is_sup x y (Sup {x, y})";
    13   br (bin_is_Sup_eq RS subst) 1;
    14   br Sup_is_Sup 1;
    15 qed "Sup_is_sup";
    16 
    17 
    18 
    19 (** product lattices **)
    20 
    21 (* pairs *)
    22 
    23 goalw thy [is_inf_def, le_prod_def] "is_inf p q (fst p && fst q, snd p && snd q)";
    24   by (Simp_tac 1);
    25   by (safe_tac (claset()));
    26   by (REPEAT_FIRST (fn i => resolve_tac [inf_lb1, inf_lb2, inf_ub_lbs] i ORELSE atac i));
    27 qed "prod_is_inf";
    28 
    29 goalw thy [is_sup_def, le_prod_def] "is_sup p q (fst p || fst q, snd p || snd q)";
    30   by (Simp_tac 1);
    31   by (safe_tac (claset()));
    32   by (REPEAT_FIRST (fn i => resolve_tac [sup_ub1, sup_ub2, sup_lb_ubs] i ORELSE atac i));
    33 qed "prod_is_sup";
    34 
    35 
    36 (* functions *)
    37 
    38 goalw thy [is_inf_def, le_fun_def] "is_inf f g (%x. f x && g x)";
    39   by (safe_tac (claset()));
    40   br inf_lb1 1;
    41   br inf_lb2 1;
    42   br inf_ub_lbs 1;
    43   by (REPEAT_FIRST (Fast_tac));
    44 qed "fun_is_inf";
    45 
    46 goalw thy [is_sup_def, le_fun_def] "is_sup f g (%x. f x || g x)";
    47   by (safe_tac (claset()));
    48   br sup_ub1 1;
    49   br sup_ub2 1;
    50   br sup_lb_ubs 1;
    51   by (REPEAT_FIRST (Fast_tac));
    52 qed "fun_is_sup";
    53 
    54 
    55 
    56 (** dual lattices **)
    57 
    58 goalw thy [is_inf_def, le_dual_def] "is_inf x y (Abs_dual (Rep_dual x || Rep_dual y))";
    59   by (stac Abs_dual_inverse' 1);
    60   by (safe_tac (claset()));
    61   br sup_ub1 1;
    62   br sup_ub2 1;
    63   br sup_lb_ubs 1;
    64   ba 1;
    65   ba 1;
    66 qed "dual_is_inf";
    67 
    68 goalw thy [is_sup_def, le_dual_def] "is_sup x y (Abs_dual (Rep_dual x && Rep_dual y))";
    69   by (stac Abs_dual_inverse' 1);
    70   by (safe_tac (claset()));
    71   br inf_lb1 1;
    72   br inf_lb2 1;
    73   br inf_ub_lbs 1;
    74   ba 1;
    75   ba 1;
    76 qed "dual_is_sup";