8 |
8 |
9 (* ------------------------------------------------------------------------ *) |
9 (* ------------------------------------------------------------------------ *) |
10 (* less_fun is a partial order on 'a => 'b *) |
10 (* less_fun is a partial order on 'a => 'b *) |
11 (* ------------------------------------------------------------------------ *) |
11 (* ------------------------------------------------------------------------ *) |
12 |
12 |
13 val prems = goalw thy [less_fun_def] "(f::'a::term =>'b::po) << f"; |
13 val prems = goalw thy [less_fun_def] "(f::'a::type =>'b::po) << f"; |
14 by (fast_tac (HOL_cs addSIs [refl_less]) 1); |
14 by (fast_tac (HOL_cs addSIs [refl_less]) 1); |
15 qed "refl_less_fun"; |
15 qed "refl_less_fun"; |
16 |
16 |
17 val prems = goalw Fun1.thy [less_fun_def] |
17 val prems = goalw Fun1.thy [less_fun_def] |
18 "[|(f1::'a::term =>'b::po) << f2; f2 << f1|] ==> f1 = f2"; |
18 "[|(f1::'a::type =>'b::po) << f2; f2 << f1|] ==> f1 = f2"; |
19 by (cut_facts_tac prems 1); |
19 by (cut_facts_tac prems 1); |
20 by (stac expand_fun_eq 1); |
20 by (stac expand_fun_eq 1); |
21 by (fast_tac (HOL_cs addSIs [antisym_less]) 1); |
21 by (fast_tac (HOL_cs addSIs [antisym_less]) 1); |
22 qed "antisym_less_fun"; |
22 qed "antisym_less_fun"; |
23 |
23 |
24 val prems = goalw Fun1.thy [less_fun_def] |
24 val prems = goalw Fun1.thy [less_fun_def] |
25 "[|(f1::'a::term =>'b::po) << f2; f2 << f3 |] ==> f1 << f3"; |
25 "[|(f1::'a::type =>'b::po) << f2; f2 << f3 |] ==> f1 << f3"; |
26 by (cut_facts_tac prems 1); |
26 by (cut_facts_tac prems 1); |
27 by (strip_tac 1); |
27 by (strip_tac 1); |
28 by (rtac trans_less 1); |
28 by (rtac trans_less 1); |
29 by (etac allE 1); |
29 by (etac allE 1); |
30 by (atac 1); |
30 by (atac 1); |