|
1 (* Title: Substitutions/utermlemmas.ML |
|
2 Author: Martin Coen, Cambridge University Computer Laboratory |
|
3 Copyright 1993 University of Cambridge |
|
4 |
|
5 For utermlemmas.thy. |
|
6 *) |
|
7 |
|
8 open UTLemmas; |
|
9 |
|
10 (***********) |
|
11 |
|
12 val utlemmas_defs = [vars_of_def,occs_def]; |
|
13 |
|
14 local fun mk_thm s = prove_goalw UTLemmas.thy utlemmas_defs s |
|
15 (fn _ => [simp_tac uterm_ss 1]) |
|
16 in val utlemmas_rews = map mk_thm |
|
17 ["vars_of(Const(c)) = {}", |
|
18 "vars_of(Var(x)) = {x}", |
|
19 "vars_of(Comb(t,u)) = vars_of(t) Un vars_of(u)", |
|
20 "t <: Const(c) = False", |
|
21 "t <: Var(x) = False", |
|
22 "t <: Comb(u,v) = (t=u | t=v | t <: u | t <: v)"]; |
|
23 end; |
|
24 |
|
25 val utlemmas_ss = pair_ss addsimps (setplus_rews @ uterm_rews @ utlemmas_rews); |
|
26 |
|
27 (**** occs irrefl ****) |
|
28 |
|
29 goal UTLemmas.thy "t <: u & u <: v --> t <: v"; |
|
30 by (uterm_ind_tac "v" 1); |
|
31 by (ALLGOALS (simp_tac utlemmas_ss)); |
|
32 by (fast_tac HOL_cs 1); |
|
33 val occs_trans = conjI RS (result() RS mp); |
|
34 |
|
35 goal UTLemmas.thy "~ t <: v --> ~ t <: u | ~ u <: v"; |
|
36 by (fast_tac (HOL_cs addIs [occs_trans]) 1); |
|
37 val contr_occs_trans = result() RS mp; |
|
38 |
|
39 goal UTLemmas.thy "t <: Comb(t,u)"; |
|
40 by (simp_tac utlemmas_ss 1); |
|
41 val occs_Comb1 = result(); |
|
42 |
|
43 goal UTLemmas.thy "u <: Comb(t,u)"; |
|
44 by (simp_tac utlemmas_ss 1); |
|
45 val occs_Comb2 = result(); |
|
46 |
|
47 goal HOL.thy "(~(P|Q)) = (~P & ~Q)"; |
|
48 by (fast_tac HOL_cs 1); |
|
49 val demorgan_disj = result(); |
|
50 |
|
51 goal UTLemmas.thy "~ t <: t"; |
|
52 by (uterm_ind_tac "t" 1); |
|
53 by (ALLGOALS (simp_tac (utlemmas_ss addsimps [demorgan_disj]))); |
|
54 by (REPEAT (resolve_tac [impI,conjI] 1 ORELSE |
|
55 (etac contrapos 1 THEN etac subst 1 THEN |
|
56 resolve_tac [occs_Comb1,occs_Comb2] 1) ORELSE |
|
57 (etac (contr_occs_trans RS disjE) 1 THEN assume_tac 2) ORELSE |
|
58 eresolve_tac ([occs_Comb1,occs_Comb2] RLN(2,[notE])) 1)); |
|
59 val occs_irrefl = result(); |
|
60 |
|
61 goal UTLemmas.thy "t <: u --> ~t=u"; |
|
62 by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1); |
|
63 val occs_irrefl2 = result() RS mp; |
|
64 |
|
65 |
|
66 (**** vars_of lemmas ****) |
|
67 |
|
68 goal UTLemmas.thy "(v : vars_of(Var(w))) = (w=v)"; |
|
69 by (simp_tac utlemmas_ss 1); |
|
70 by (fast_tac HOL_cs 1); |
|
71 val vars_var_iff = result(); |
|
72 |
|
73 goal UTLemmas.thy "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)"; |
|
74 by (uterm_ind_tac "t" 1); |
|
75 by (ALLGOALS (simp_tac utlemmas_ss)); |
|
76 by (fast_tac HOL_cs 1); |
|
77 val vars_iff_occseq = result(); |