author | wenzelm |
Mon, 03 Nov 1997 14:06:27 +0100 | |
changeset 4098 | 71e05eb27fb6 |
parent 3073 | 88366253a09a |
child 4377 | 2cba48b0f1c4 |
permissions | -rw-r--r-- |
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(* Title: HOL/IOA/NTP/Impl.ML |
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ID: $Id$ |
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Author: Tobias Nipkow & Konrad Slind |
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Copyright 1994 TU Muenchen |
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|
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The implementation --- Invariants |
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*) |
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|
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|
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Addsimps [Let_def]; |
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|
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open Abschannel Impl; |
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|
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val impl_ioas = |
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[Impl.impl_def, |
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Sender.sender_ioa_def, |
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Receiver.receiver_ioa_def, |
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srch_ioa_thm RS eq_reflection, |
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rsch_ioa_thm RS eq_reflection]; |
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|
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val transitions = [Sender.sender_trans_def, Receiver.receiver_trans_def, |
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srch_trans_def, rsch_trans_def]; |
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Addsimps [ioa_triple_proj, starts_of_par, trans_of_par4, |
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in_sender_asig, in_receiver_asig, in_srch_asig, |
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in_rsch_asig]; |
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Addcongs [let_weak_cong]; |
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goal Impl.thy |
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"fst(x) = sen(x) & \ |
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\ fst(snd(x)) = rec(x) & \ |
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\ fst(snd(snd(x))) = srch(x) & \ |
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\ snd(snd(snd(x))) = rsch(x)"; |
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by(simp_tac (simpset() addsimps |
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[sen_def,rec_def,srch_def,rsch_def]) 1); |
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Addsimps [result()]; |
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goal Impl.thy "a:actions(sender_asig) \ |
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\ | a:actions(receiver_asig) \ |
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\ | a:actions(srch_asig) \ |
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\ | a:actions(rsch_asig)"; |
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by(Action.action.induct_tac "a" 1); |
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by(ALLGOALS (Simp_tac)); |
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Addsimps [result()]; |
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Delsimps [split_paired_All]; |
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(* Three Simp_sets in different sizes |
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---------------------------------------------- |
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1) simpset() does not unfold the transition relations |
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2) ss unfolds transition relations |
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3) renname_ss unfolds transitions and the abstract channel *) |
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val ss = (simpset() addcongs [if_weak_cong] |
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addsimps transitions); |
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val rename_ss = (ss addsimps unfold_renaming); |
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val tac = asm_simp_tac ((ss addcongs [conj_cong]) |
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setloop (split_tac [expand_if])); |
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val tac_ren = asm_simp_tac ((rename_ss addcongs [conj_cong]) |
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setloop (split_tac [expand_if])); |
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(* INVARIANT 1 *) |
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goalw Impl.thy impl_ioas "invariant impl_ioa inv1"; |
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by (rtac invariantI 1); |
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by(asm_full_simp_tac (simpset() |
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addsimps [inv1_def, hdr_sum_def, Sender.srcvd_def, |
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Sender.ssent_def, Receiver.rsent_def,Receiver.rrcvd_def]) 1); |
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|
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by(simp_tac (simpset() delsimps [trans_of_par4] |
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addsimps [fork_lemma,inv1_def]) 1); |
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|
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(* Split proof in two *) |
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by (rtac conjI 1); |
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|
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(* First half *) |
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by(asm_full_simp_tac (simpset() addsimps [Impl.inv1_def]) 1); |
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by (rtac Action.action.induct 1); |
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|
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by (EVERY1[tac, tac, tac, tac]); |
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by (tac 1); |
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by (tac_ren 1); |
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(* 5 + 1 *) |
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|
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by (tac 1); |
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by (tac_ren 1); |
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|
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(* 4 + 1 *) |
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by(EVERY1[tac, tac, tac, tac]); |
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|
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(* Now the other half *) |
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by(asm_full_simp_tac (simpset() addsimps [Impl.inv1_def]) 1); |
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by (rtac Action.action.induct 1); |
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by(EVERY1[tac, tac]); |
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|
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(* detour 1 *) |
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by (tac 1); |
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by (tac_ren 1); |
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by (rtac impI 1); |
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by (REPEAT (etac conjE 1)); |
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by (asm_simp_tac (simpset() addsimps [hdr_sum_def, Multiset.count_def, |
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Multiset.countm_nonempty_def] |
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setloop (split_tac [expand_if])) 1); |
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(* detour 2 *) |
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by (tac 1); |
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by (tac_ren 1); |
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by (rtac impI 1); |
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by (REPEAT (etac conjE 1)); |
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by (asm_full_simp_tac (simpset() addsimps [Impl.hdr_sum_def, |
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Multiset.count_def, |
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Multiset.countm_nonempty_def, |
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Multiset.delm_nonempty_def, |
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left_plus_cancel, |
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left_plus_cancel_inside_succ, |
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unzero_less] |
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setloop (split_tac [expand_if])) 1); |
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by (rtac allI 1); |
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by (rtac conjI 1); |
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by (rtac impI 1); |
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by (hyp_subst_tac 1); |
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by (rtac (pred_suc RS mp RS sym RS iffD2) 1); |
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by (dtac less_le_trans 1); |
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by (cut_facts_tac [rewrite_rule[Packet.hdr_def] |
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eq_packet_imp_eq_hdr RS countm_props] 1);; |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
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|
137 |
by (assume_tac 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
138 |
by (assume_tac 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
139 |
|
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
140 |
by (rtac (countm_done_delm RS mp RS sym) 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
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|
141 |
by (rtac refl 1); |
4098 | 142 |
by (asm_simp_tac (simpset() addsimps [Multiset.count_def]) 1); |
3073
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Old NTP files now running under the IOA meta theory based on HOLCF;
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parents:
diff
changeset
|
143 |
|
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
144 |
by (rtac impI 1); |
4098 | 145 |
by (asm_full_simp_tac (simpset() addsimps [neg_flip]) 1); |
3073
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
146 |
by (hyp_subst_tac 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
147 |
by (rtac countm_spurious_delm 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
148 |
by (Simp_tac 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
149 |
|
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parents:
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|
150 |
by (EVERY1[tac, tac, tac, tac, tac, tac]); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
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parents:
diff
changeset
|
151 |
|
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parents:
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|
152 |
qed "inv1"; |
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parents:
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|
153 |
|
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parents:
diff
changeset
|
154 |
|
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mueller
parents:
diff
changeset
|
155 |
|
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parents:
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|
156 |
(* INVARIANT 2 *) |
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|
157 |
|
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parents:
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|
158 |
goal Impl.thy "invariant impl_ioa inv2"; |
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parents:
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|
159 |
|
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mueller
parents:
diff
changeset
|
160 |
by (rtac invariantI1 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
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|
161 |
(* Base case *) |
4098 | 162 |
by (asm_full_simp_tac (simpset() addsimps (inv2_def :: |
3073
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parents:
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|
163 |
(receiver_projections |
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parents:
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|
164 |
@ sender_projections @ impl_ioas))) |
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parents:
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|
165 |
1); |
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parents:
diff
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|
166 |
|
4098 | 167 |
by (asm_simp_tac (simpset() addsimps impl_ioas) 1); |
3073
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mueller
parents:
diff
changeset
|
168 |
by (Action.action.induct_tac "a" 1); |
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parents:
diff
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|
169 |
|
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parents:
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|
170 |
(* 10 cases. First 4 are simple, since state doesn't change *) |
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parents:
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|
171 |
|
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parents:
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|
172 |
val tac2 = asm_full_simp_tac (ss addsimps [inv2_def]); |
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parents:
diff
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|
173 |
|
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parents:
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|
174 |
(* 10 - 7 *) |
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mueller
parents:
diff
changeset
|
175 |
by (EVERY1[tac2,tac2,tac2,tac2]); |
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parents:
diff
changeset
|
176 |
(* 6 *) |
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parents:
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|
177 |
by(forward_tac [rewrite_rule [Impl.inv1_def] |
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parents:
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|
178 |
(inv1 RS invariantE) RS conjunct1] 1); |
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parents:
diff
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|
179 |
(* 6 - 5 *) |
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mueller
parents:
diff
changeset
|
180 |
by (EVERY1[tac2,tac2]); |
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mueller
parents:
diff
changeset
|
181 |
|
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parents:
diff
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|
182 |
(* 4 *) |
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mueller
parents:
diff
changeset
|
183 |
by (forward_tac [rewrite_rule [Impl.inv1_def] |
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parents:
diff
changeset
|
184 |
(inv1 RS invariantE) RS conjunct1] 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
185 |
by (tac2 1); |
4098 | 186 |
by (fast_tac (claset() addDs [add_leD1,leD]) 1); |
3073
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parents:
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|
187 |
|
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parents:
diff
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|
188 |
(* 3 *) |
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mueller
parents:
diff
changeset
|
189 |
by (forward_tac [rewrite_rule [Impl.inv1_def] (inv1 RS invariantE)] 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
190 |
|
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
191 |
by (tac2 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
192 |
by (fold_tac [rewrite_rule [Packet.hdr_def]Impl.hdr_sum_def]); |
4098 | 193 |
by (fast_tac (claset() addDs [add_leD1,leD]) 1); |
3073
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
194 |
|
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mueller
parents:
diff
changeset
|
195 |
(* 2 *) |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
196 |
by (tac2 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
197 |
by(forward_tac [rewrite_rule [Impl.inv1_def] |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
198 |
(inv1 RS invariantE) RS conjunct1] 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
199 |
by (rtac impI 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
200 |
by (rtac impI 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
201 |
by (REPEAT (etac conjE 1)); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
202 |
by (dres_inst_tac [("k","count (rsch s) (~sbit(sen s))")] |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
203 |
(standard(leq_add_leq RS mp)) 1); |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
204 |
by (Asm_full_simp_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
205 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
206 |
(* 1 *) |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
207 |
by (tac2 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
208 |
by(forward_tac [rewrite_rule [Impl.inv1_def] |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
209 |
(inv1 RS invariantE) RS conjunct2] 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
210 |
by (rtac impI 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
211 |
by (rtac impI 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
212 |
by (REPEAT (etac conjE 1)); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
213 |
by (fold_tac [rewrite_rule[Packet.hdr_def]Impl.hdr_sum_def]); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
214 |
by (dres_inst_tac [("k","hdr_sum (srch s) (sbit(sen s))")] |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
215 |
(standard(leq_add_leq RS mp)) 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
216 |
by (Asm_full_simp_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
217 |
qed "inv2"; |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
218 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
219 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
220 |
(* INVARIANT 3 *) |
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
221 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
222 |
goal Impl.thy "invariant impl_ioa inv3"; |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
223 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
224 |
by (rtac invariantI 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
225 |
(* Base case *) |
4098 | 226 |
by (asm_full_simp_tac (simpset() addsimps |
3073
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mueller
parents:
diff
changeset
|
227 |
(Impl.inv3_def :: (receiver_projections |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
228 |
@ sender_projections @ impl_ioas))) 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
229 |
|
4098 | 230 |
by (asm_simp_tac (simpset() addsimps impl_ioas) 1); |
3073
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Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
231 |
by (Action.action.induct_tac "a" 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
232 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
233 |
val tac3 = asm_full_simp_tac (ss addsimps [inv3_def] |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
234 |
setloop (split_tac [expand_if])); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
235 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
236 |
(* 10 - 8 *) |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
237 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
238 |
by (EVERY1[tac3,tac3,tac3]); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
239 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
240 |
by (tac_ren 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
241 |
by (strip_tac 1 THEN REPEAT (etac conjE 1)); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
242 |
by (hyp_subst_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
243 |
by (etac exE 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
244 |
by (Asm_full_simp_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
245 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
246 |
(* 7 *) |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
247 |
by (tac3 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
248 |
by (tac_ren 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
249 |
by (Fast_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
250 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
251 |
(* 6 - 3 *) |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
252 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
253 |
by (EVERY1[tac3,tac3,tac3,tac3]); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
254 |
|
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
255 |
(* 2 *) |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
256 |
by (asm_full_simp_tac ss 1); |
4098 | 257 |
by (simp_tac (simpset() addsimps [inv3_def]) 1); |
3073
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
258 |
by (strip_tac 1 THEN REPEAT (etac conjE 1)); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
259 |
by (rtac (imp_or_lem RS iffD2) 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
260 |
by (rtac impI 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
261 |
by (forward_tac [rewrite_rule [Impl.inv2_def] (inv2 RS invariantE)] 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
262 |
by (Asm_full_simp_tac 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
263 |
by (REPEAT (etac conjE 1)); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
264 |
by (res_inst_tac [("j","count (ssent(sen s)) (~sbit(sen s))"), |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
265 |
("k","count (rsent(rec s)) (sbit(sen s))")] le_trans 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
266 |
by (forward_tac [rewrite_rule [inv1_def] |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
267 |
(inv1 RS invariantE) RS conjunct2] 1); |
4098 | 268 |
by (asm_full_simp_tac (simpset() addsimps |
3073
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
269 |
[hdr_sum_def, Multiset.count_def]) 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
270 |
by (rtac (less_eq_add_cong RS mp RS mp) 1); |
88366253a09a
Old NTP files now running under the IOA meta theory based on HOLCF;
mueller
parents:
diff
changeset
|
271 |
by (rtac countm_props 1); |
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272 |
by (Simp_tac 1); |
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273 |
by (rtac countm_props 1); |
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274 |
by (Simp_tac 1); |
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275 |
by (assume_tac 1); |
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276 |
|
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277 |
(* 1 *) |
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278 |
by (tac3 1); |
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279 |
by (strip_tac 1 THEN REPEAT (etac conjE 1)); |
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280 |
by (rtac (imp_or_lem RS iffD2) 1); |
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281 |
by (rtac impI 1); |
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282 |
by (forward_tac [rewrite_rule [Impl.inv2_def] (inv2 RS invariantE)] 1); |
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283 |
by (Asm_full_simp_tac 1); |
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284 |
by (REPEAT (etac conjE 1)); |
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285 |
by (dtac mp 1); |
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286 |
by (assume_tac 1); |
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287 |
by (etac allE 1); |
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288 |
by (dtac (imp_or_lem RS iffD1) 1); |
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289 |
by (dtac mp 1); |
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290 |
by (assume_tac 1); |
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291 |
by (assume_tac 1); |
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292 |
qed "inv3"; |
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293 |
|
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294 |
|
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295 |
(* INVARIANT 4 *) |
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296 |
|
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297 |
goal Impl.thy "invariant impl_ioa inv4"; |
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298 |
|
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299 |
by (rtac invariantI 1); |
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300 |
(* Base case *) |
4098 | 301 |
by (asm_full_simp_tac (simpset() addsimps |
3073
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302 |
(Impl.inv4_def :: (receiver_projections |
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303 |
@ sender_projections @ impl_ioas))) 1); |
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304 |
|
4098 | 305 |
by (asm_simp_tac (simpset() addsimps impl_ioas) 1); |
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306 |
by (Action.action.induct_tac "a" 1); |
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307 |
|
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308 |
val tac4 = asm_full_simp_tac (ss addsimps [inv4_def] |
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309 |
setloop (split_tac [expand_if])); |
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310 |
|
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311 |
(* 10 - 2 *) |
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312 |
|
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313 |
by (EVERY1[tac4,tac4,tac4,tac4,tac4,tac4,tac4,tac4,tac4]); |
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314 |
|
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315 |
(* 2 b *) |
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316 |
|
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317 |
by (strip_tac 1 THEN REPEAT (etac conjE 1)); |
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318 |
by(forward_tac [rewrite_rule [Impl.inv2_def] |
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319 |
(inv2 RS invariantE)] 1); |
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320 |
by (tac4 1); |
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321 |
by (Asm_full_simp_tac 1); |
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|
322 |
|
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323 |
(* 1 *) |
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324 |
by (tac4 1); |
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325 |
by (strip_tac 1 THEN REPEAT (etac conjE 1)); |
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326 |
by (rtac ccontr 1); |
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|
327 |
by(forward_tac [rewrite_rule [Impl.inv2_def] |
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|
328 |
(inv2 RS invariantE)] 1); |
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|
329 |
by(forward_tac [rewrite_rule [Impl.inv3_def] |
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|
330 |
(inv3 RS invariantE)] 1); |
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|
331 |
by (Asm_full_simp_tac 1); |
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|
332 |
by (eres_inst_tac [("x","m")] allE 1); |
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|
333 |
by (dtac less_le_trans 1); |
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|
334 |
by (dtac (left_add_leq RS mp) 1); |
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|
335 |
by (Asm_full_simp_tac 1); |
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|
336 |
by (Asm_full_simp_tac 1); |
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|
337 |
qed "inv4"; |
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|
338 |
|
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|
339 |
|
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|
340 |
(* rebind them *) |
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|
341 |
|
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|
342 |
val inv1 = rewrite_rule [Impl.inv1_def] (inv1 RS invariantE); |
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|
343 |
val inv2 = rewrite_rule [Impl.inv2_def] (inv2 RS invariantE); |
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|
344 |
val inv3 = rewrite_rule [Impl.inv3_def] (inv3 RS invariantE); |
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|
345 |
val inv4 = rewrite_rule [Impl.inv4_def] (inv4 RS invariantE); |