7 open Types; |
7 open Types; |
8 |
8 |
9 val te_owrE = |
9 val te_owrE = |
10 TyEnv.mk_cases TyEnv.con_defs "te_owr(te,f,t):TyEnv"; |
10 TyEnv.mk_cases TyEnv.con_defs "te_owr(te,f,t):TyEnv"; |
11 |
11 |
12 Goalw TyEnv.con_defs "rank(te) < rank(te_owr(te,x,t))"; |
12 Goal "te_app(te_owr(te,x,t),x) = t"; |
13 by (simp_tac rank_ss 1); |
13 by (Simp_tac 1); |
14 qed "rank_te_owr1"; |
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15 |
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16 Goal "te_rec(te_emp,c_te_emp,f_te_owr) = c_te_emp"; |
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17 by (rtac (te_rec_def RS def_Vrec RS trans) 1); |
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18 by (simp_tac (simpset() addsimps rank_te_owr1::TyEnv.case_eqns) 1); |
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19 qed "te_rec_emp"; |
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20 |
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21 Goal " te_rec(te_owr(te,x,t),c_te_emp,f_te_owr) = \ |
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22 \ f_te_owr(te,x,t,te_rec(te,c_te_emp,f_te_owr))"; |
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23 by (rtac (te_rec_def RS def_Vrec RS trans) 1); |
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24 by (simp_tac (rank_ss addsimps rank_te_owr1::TyEnv.case_eqns) 1); |
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25 qed "te_rec_owr"; |
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26 |
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27 Goalw [te_dom_def] "te_dom(te_emp) = 0"; |
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28 by (simp_tac (simpset() addsimps [te_rec_emp]) 1); |
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29 qed "te_dom_emp"; |
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30 |
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31 Goalw [te_dom_def] "te_dom(te_owr(te,x,v)) = te_dom(te) Un {x}"; |
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32 by (simp_tac (simpset() addsimps [te_rec_owr]) 1); |
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33 qed "te_dom_owr"; |
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34 |
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35 Goalw [te_app_def] "te_app(te_owr(te,x,t),x) = t"; |
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36 by (simp_tac (simpset() addsimps [te_rec_owr]) 1); |
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37 qed "te_app_owr1"; |
14 qed "te_app_owr1"; |
38 |
15 |
39 Goalw [te_app_def] |
16 Goal "x ~= y ==> te_app(te_owr(te,x,t),y) = te_app(te,y)"; |
40 "x ~= y ==> te_app(te_owr(te,x,t),y) = te_app(te,y)"; |
17 by Auto_tac; |
41 by (asm_simp_tac (simpset() addsimps [te_rec_owr,(not_sym RS if_not_P)]) 1); |
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42 qed "te_app_owr2"; |
18 qed "te_app_owr2"; |
43 |
19 |
44 Goal "[| te:TyEnv; x:ExVar; x:te_dom(te) |] ==> te_app(te,x):Ty"; |
20 Goal "[| te:TyEnv; x:ExVar; x:te_dom(te) |] ==> te_app(te,x):Ty"; |
45 by (res_inst_tac [("P","x:te_dom(te)")] impE 1); |
21 by (res_inst_tac [("P","x:te_dom(te)")] impE 1); |
46 by (assume_tac 2); |
22 by (assume_tac 2); |
47 by (assume_tac 2); |
23 by (assume_tac 2); |
48 by (etac TyEnv.induct 1); |
24 by (etac TyEnv.induct 1); |
49 by (simp_tac (simpset() addsimps [te_dom_emp]) 1); |
25 by (Simp_tac 1); |
50 by (rtac impI 1); |
26 by (case_tac "xa = x" 1); |
51 by (rtac (excluded_middle RS disjE) 1); |
27 by Auto_tac; |
52 by (stac te_app_owr2 1); |
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53 by (assume_tac 1); |
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54 by (asm_full_simp_tac (simpset() addsimps [te_dom_owr]) 1); |
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55 by (Fast_tac 1); |
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56 by (asm_simp_tac (simpset() addsimps [te_app_owr1]) 1); |
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57 qed "te_appI"; |
28 qed "te_appI"; |
58 |
29 |
59 |
30 |
60 |
31 |
61 |
32 |