src/HOL/AxClasses/Lattice/LatMorph.ML
author paulson
Wed Nov 05 13:23:46 1997 +0100 (1997-11-05)
changeset 4153 e534c4c32d54
parent 4091 771b1f6422a8
child 5069 3ea049f7979d
permissions -rw-r--r--
Ran expandshort, especially to introduce Safe_tac
     1 
     2 open LatMorph;
     3 
     4 
     5 (** monotone functions vs. "&&"- / "||"-semi-morphisms **)
     6 
     7 goalw thy [is_mono_def] "is_mono f = (ALL x y. f (x && y) [= f x && f y)";
     8   by Safe_tac;
     9   (*==> (level 1)*)
    10     by (stac le_inf_eq 1);
    11     by (rtac conjI 1);
    12     by (Step_tac 1);
    13     by (Step_tac 1);
    14     by (etac mp 1);
    15     by (rtac inf_lb1 1);
    16     by (Step_tac 1);
    17     by (Step_tac 1);
    18     by (etac mp 1);
    19     by (rtac inf_lb2 1);
    20   (*==> (level 11)*)
    21     by (rtac (conjI RS (le_trans RS mp)) 1);
    22     by (rtac inf_lb2 2);
    23     by (subgoal_tac "x && y = x" 1);
    24     by (etac subst 1);
    25     by (Fast_tac 1);
    26     by (stac inf_connect 1);
    27     by (assume_tac 1);
    28 qed "mono_inf_eq";
    29 
    30 goalw thy [is_mono_def] "is_mono f = (ALL x y. f x || f y [= f (x || y))";
    31   by Safe_tac;
    32   (*==> (level 1)*)
    33     by (stac ge_sup_eq 1);
    34     by (rtac conjI 1);
    35     by (Step_tac 1);
    36     by (Step_tac 1);
    37     by (etac mp 1);
    38     by (rtac sup_ub1 1);
    39     by (Step_tac 1);
    40     by (Step_tac 1);
    41     by (etac mp 1);
    42     by (rtac sup_ub2 1);
    43   (*==> (level 11)*)
    44     by (rtac (conjI RS (le_trans RS mp)) 1);
    45     by (rtac sup_ub1 1);
    46     by (subgoal_tac "x || y = y" 1);
    47     by (etac subst 1);
    48     by (Fast_tac 1);
    49     by (stac sup_connect 1);
    50     by (assume_tac 1);
    51 qed "mono_sup_eq";
    52 
    53