source: src/ASM/AssemblyProofSplit.ma @ 1952

Last change on this file since 1952 was 1952, checked in by sacerdot, 8 years ago

AssemblyProof? splitted.

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1include "ASM/AssemblyProof.ma".
2include alias "arithmetics/nat.ma".
3include alias "basics/logic.ma".
4
5theorem main_thm:
6  ∀M.
7  ∀M'.
8  ∀cm.
9  ∀ps.
10  ∀sigma.
11  ∀policy.
12    next_internal_pseudo_address_map M cm ps = Some … M' →
13      ∃n. execute n … (status_of_pseudo_status M … ps sigma policy) =
14        status_of_pseudo_status M' …
15          (execute_1_pseudo_instruction (ticks_of cm sigma policy) cm ps) sigma policy.
16  #M #M' * #preamble #instr_list #ps #sigma #policy
17  change with (next_internal_pseudo_address_map0 ????? = ? → ?)
18  @(pose … (program_counter ?? ps)) #ppc #EQppc
19  generalize in match (fetch_assembly_pseudo2 〈preamble,instr_list〉 sigma policy ppc) in ⊢ ?;
20  @pair_elim #labels #costs #H0 normalize nodelta
21  @pair_elim #assembled #costs' #EQ1 normalize nodelta
22  @pair_elim #pi #newppc #EQ2 normalize nodelta
23  @(pose … (λx. sigma (address_of_word_labels_code_mem instr_list x))) #lookup_labels #EQlookup_labels
24  @(pose … (λx. lookup_def … (construct_datalabels preamble) x (zero 16))) #lookup_datalabels #EQlookup_datalabels
25  whd in match execute_1_pseudo_instruction; normalize nodelta
26  whd in match ticks_of; normalize nodelta <EQppc #H2 >EQ2 normalize nodelta
27  lapply (snd_fetch_pseudo_instruction instr_list ppc) >EQ2 #EQnewppc >EQnewppc
28  lapply (snd_assembly_1_pseudoinstruction_ok 〈preamble,instr_list〉 … policy … ppc pi … EQlookup_labels EQlookup_datalabels ?)
29  [>EQ2 %]
30  inversion pi
31  [2,3: (* Comment, Cost *)
32    #ARG #EQ
33    #H3 normalize nodelta in H3; normalize in match (assembly_1_pseudoinstruction ??????) in H3;
34    whd in ⊢ (??%? → ?); @Some_Some_elim #MAP <MAP
35    whd in match (execute_1_pseudo_instruction0 ?????);
36    %{0} @split_eq_statusCSC: this works :-) (lapply H3 -H3 letin sixteen ≝ 16 #H3 // /demod/)
37   CSC: STOP HERE, was // but requires -H3 because of 16!
38   ⇒ CHANGE TO AVOID \fst and \pi1! (*
39   try (<H3 -H0 -H3 //)
40   [ <add_zero in H3; #H3 >H3 -H0 -H3 //
41   | -H0 -H3 /demod/*)
42  |4: (* Jmp *) #label whd in ⊢ (??%? → ???% → ?)
43   @Some_Some_elim #MAP cases (pol ?) normalize nodelta
44       [3: (* long *) #EQ3 @(Some_Some_elim ????? EQ3) #EQ3'
45         whd in match eject normalize nodelta >EQ3' in ⊢ (% → ?) whd in ⊢ (% → ?)
46         @pair_elim' * #instr #newppc' #ticks #EQ4       
47         * * #H2a #H2b whd in ⊢ (% → ?) #H2
48         >H2b >(eq_instruction_to_eq … H2a)
49         #EQ %[@1]
50         <MAP >(eq_bv_eq … H2) >EQ
51         whd in ⊢ (??%?) >EQ4 whd in ⊢ (??%?)
52         cases ps in EQ4; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXX >XXX %
53         whd in ⊢ (??%?)
54         whd in ⊢ (??(match ?%? with [_ ⇒ ?])?)
55         cases ps in EQ0 ⊢ %; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXXX >XXXX %
56  |6: (* Mov *) #arg1 #arg2
57       #H1 #H2 #EQ %[@1]
58       normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
59       change in ⊢ (? → ??%?) with (execute_1_0 ??)
60       cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
61       * * #H2a #H2b whd in ⊢ (% → ?) #H2c
62       >H2b >(eq_instruction_to_eq … H2a)
63       generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?);
64       @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1; whd in ⊢ (???% → ??%?)
65       @(list_addressing_mode_tags_elim_prop … arg2) whd try % -arg2; #ARG2
66       normalize nodelta;
67       [1,2,3,4,5,6,7,8: cases (add_8_with_carry ???) |*: cases (sub_8_with_carry ???)]
68       #result #flags
69       #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) %
70  |5: (* Call *) #label #MAP
71      generalize in match (option_destruct_Some ??? MAP) -MAP; #MAP <MAP -MAP;
72      whd in ⊢ (???% → ?) cases (pol ?) normalize nodelta;
73       [ (* short *) #abs @⊥ destruct (abs)
74       |3: (* long *) #H1 #H2 #EQ %[@1]
75           (* normalize in H1; !!!*) generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
76           change in ⊢ (? → ??%?) with (execute_1_0 ??)
77           cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
78           * * #H2a #H2b whd in ⊢ (% → ?) #H2c
79           >H2b >(eq_instruction_to_eq … H2a)
80           generalize in match EQ; -EQ;
81           whd in ⊢ (???% → ??%?);
82           generalize in match (refl … (half_add 8 (get_8051_sfr ? ps SFR_SP) (bitvector_of_nat ? 1))) cases (half_add ???) in ⊢ (??%? → %) #carry #new_sp #EQ1 normalize nodelta;
83           >(eq_bv_eq … H2c)
84           change with
85            ((?=let 〈ppc_bu,ppc_bl〉 ≝ split bool 8 8 newppc in ?) →
86                (let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc) in ?)=?)
87           generalize in match (refl … (split … 8 8 newppc)) cases (split bool 8 8 newppc) in ⊢ (??%? → %) #ppc_bu #ppc_bl #EQppc
88           generalize in match (refl … (split … 8 8 (sigma 〈preamble,instr_list〉 pol newppc))) cases (split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc)) in ⊢ (??%? → %) #pc_bu #pc_bl #EQpc normalize nodelta;
89           >get_8051_sfr_write_at_stack_pointer >get_8051_sfr_write_at_stack_pointer
90           >get_8051_sfr_set_8051_sfr >get_8051_sfr_set_8051_sfr
91           generalize in match (refl … (half_add ? new_sp (bitvector_of_nat ? 1))) cases (half_add ???) in ⊢ (??%? → %) #carry' #new_sp' #EQ2 normalize nodelta;
92           #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c)
93           @split_eq_status;
94            [ >code_memory_write_at_stack_pointer whd in ⊢ (??%?)
95              >code_memory_write_at_stack_pointer %
96            | >set_program_counter_set_low_internal_ram
97              >set_clock_set_low_internal_ram
98              @low_internal_ram_write_at_stack_pointer
99               [ >EQ0 @pol | % | %
100               | @(pair_destruct_2 … EQ1)
101               | @(pair_destruct_2 … EQ2)
102               | >(pair_destruct_1 ????? EQpc)
103                 >(pair_destruct_2 ????? EQpc)
104                 @split_elim #x #y #H <H -x y H;
105                 >(pair_destruct_1 ????? EQppc)
106                 >(pair_destruct_2 ????? EQppc)
107                 @split_elim #x #y #H <H -x y H;
108                 >EQ0 % ]
109            | >set_low_internal_ram_set_high_internal_ram
110              >set_program_counter_set_high_internal_ram
111              >set_clock_set_high_internal_ram
112              @high_internal_ram_write_at_stack_pointer
113               [ >EQ0 @pol | % | %
114               | @(pair_destruct_2 … EQ1)
115               | @(pair_destruct_2 … EQ2)
116               | >(pair_destruct_1 ????? EQpc)
117                 >(pair_destruct_2 ????? EQpc)
118                 @split_elim #x #y #H <H -x y H;
119                 >(pair_destruct_1 ????? EQppc)
120                 >(pair_destruct_2 ????? EQppc)
121                 @split_elim #x #y #H <H -x y H;
122                 >EQ0 % ]           
123            | >external_ram_write_at_stack_pointer whd in ⊢ (??%?)
124              >external_ram_write_at_stack_pointer whd in ⊢ (???%)
125              >external_ram_write_at_stack_pointer whd in ⊢ (???%)
126              >external_ram_write_at_stack_pointer %
127            | change with (? = sigma ?? (address_of_word_labels_code_mem (\snd (code_memory ? ps)) ?))
128              >EQ0 %
129            | >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (??%?)
130              >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (???%)
131              >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (???%)
132              >special_function_registers_8051_write_at_stack_pointer %
133            | >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (??%?)
134              >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (???%)
135              >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (???%)
136              >special_function_registers_8052_write_at_stack_pointer %
137            | >p1_latch_write_at_stack_pointer whd in ⊢ (??%?)
138              >p1_latch_write_at_stack_pointer whd in ⊢ (???%)
139              >p1_latch_write_at_stack_pointer whd in ⊢ (???%)
140              >p1_latch_write_at_stack_pointer %
141            | >p3_latch_write_at_stack_pointer whd in ⊢ (??%?)
142              >p3_latch_write_at_stack_pointer whd in ⊢ (???%)
143              >p3_latch_write_at_stack_pointer whd in ⊢ (???%)
144              >p3_latch_write_at_stack_pointer %
145            | >clock_write_at_stack_pointer whd in ⊢ (??%?)
146              >clock_write_at_stack_pointer whd in ⊢ (???%)
147              >clock_write_at_stack_pointer whd in ⊢ (???%)
148              >clock_write_at_stack_pointer %]
149       (*| (* medium *)  #H1 #H2 #EQ %[@1] generalize in match H1; -H1;
150         @pair_elim' #fst_5_addr #rest_addr #EQ1
151         @pair_elim' #fst_5_pc #rest_pc #EQ2
152         generalize in match (refl … (eq_bv … fst_5_addr fst_5_pc))
153         cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta; #EQ3 #TEQ [2: destruct (TEQ)]
154         generalize in match (option_destruct_Some ??? TEQ) -TEQ; #K1 >K1 in H2; whd in ⊢ (% → ?)
155         change in ⊢ (? →??%?) with (execute_1_0 ??)
156         @pair_elim' * #instr #newppc' #ticks #EQn
157          * * #H2a #H2b whd in ⊢ (% → ?) #H2c >H2b >(eq_instruction_to_eq … H2a) whd in ⊢ (??%?)
158          generalize in match EQ; -EQ; normalize nodelta; >(eq_bv_eq … H2c)
159          @pair_elim' #carry #new_sp change with (half_add ? (get_8051_sfr ? ps ?) ? = ? → ?) #EQ4
160          @split_elim' #pc_bu #pc_bl >program_counter_set_8051_sfr XXX change with (newppc = ?) #EQ5
161          @pair_elim' #carry' #new_sp' #EQ6 normalize nodelta; #EQx >EQx -EQx;
162          change in ⊢ (??(match ????% with [_ ⇒ ?])?) with (sigma … newppc)
163          @split_elim' #pc_bu' #pc_bl' #EQ7 change with (newppc' = ? → ?)
164          >get_8051_sfr_set_8051_sfr
165         
166          whd in EQ:(???%) ⊢ ? >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) whd in ⊢ (??%?)
167           change with ((let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 newppc) in ?)=?)
168           generalize in match (refl … (split bool 8 8 (sigma 〈preamble,instr_list〉 newppc)))
169           cases (split ????) in ⊢ (??%? → %) #pc_bu #pc_bl normalize nodelta; #EQ4
170           generalize in match (refl … (split bool 4 4 pc_bu))
171           cases (split ????) in ⊢ (??%? → %) #nu #nl normalize nodelta; #EQ5
172           generalize in match (refl … (split bool 3 8 rest_addr))
173           cases (split ????) in ⊢ (??%? → %) #relevant1 #relevant2 normalize nodelta; #EQ6
174           change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma … newppc) ? in ?) = ?)
175           generalize in match
176            (refl …
177             (half_add 16 (sigma 〈preamble,instr_list〉 newppc)
178             ((nu@@get_index' bool 0 3 nl:::relevant1)@@relevant2)))
179           cases (half_add ???) in ⊢ (??%? → %) #carry #new_pc normalize nodelta; #EQ7
180           @split_eq_status try %
181            [ change with (? = sigma ? (address_of_word_labels ps label))
182              (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *)
183            | whd in ⊢ (??%%) whd in ⊢ (??(?%?)?) whd in ⊢ (??(?(match ?(?%)? with [_ ⇒ ?])?)?)
184              @(bitvector_3_elim_prop … (\fst (split bool 3 8 rest_addr))) %]] *)]
185  |4: (* Jmp *) #label #MAP
186      generalize in match (option_destruct_Some ??? MAP) -MAP; #MAP >MAP -MAP;
187      whd in ⊢ (???% → ?) cases (pol ?) normalize nodelta;
188       [3: (* long *) #H1 #H2 #EQ %[@1]
189           (* normalize in H1; !!!*) generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
190           change in ⊢ (? → ??%?) with (execute_1_0 ??)
191           cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
192           * * #H2a #H2b whd in ⊢ (% → ?) #H2c
193           >H2b >(eq_instruction_to_eq … H2a)
194           generalize in match EQ; -EQ;
195           #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c)
196           cases ps in EQ0 ⊢ %; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXXX >XXXX %
197       |1: (* short *) #H1 #H2 #EQ %[@1] generalize in match H1; -H1;
198           generalize in match
199            (refl ?
200             (sub_16_with_carry
201              (sigma 〈preamble,instr_list〉 pol (program_counter … ps))
202              (sigma 〈preamble,instr_list〉 pol (address_of_word_labels_code_mem instr_list label))
203              false))
204           cases (sub_16_with_carry ???) in ⊢ (??%? → %); #results #flags normalize nodelta;
205           generalize in match (refl … (split … 8 8 results)) cases (split ????) in ⊢ (??%? → %) #upper #lower normalize nodelta;
206           generalize in match (refl … (eq_bv … upper (zero 8))) cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta;
207           #EQ1 #EQ2 #EQ3 #H1 [2: @⊥ destruct (H1)]
208           generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
209           change in ⊢ (? → ??%?) with (execute_1_0 ??)
210           cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
211           * * #H2a #H2b whd in ⊢ (% → ?) #H2c
212           >H2b >(eq_instruction_to_eq … H2a)
213           generalize in match EQ; -EQ;
214           whd in ⊢ (???% → ?);
215           #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c)
216           change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma ???) ? in ?) = ?)
217           generalize in match (refl … (half_add 16 (sigma 〈preamble,instr_list〉 pol newppc) (sign_extension lower)))
218           cases (half_add ???) in ⊢ (??%? → %) #carry #newpc normalize nodelta #EQ4
219           @split_eq_status try % change with (newpc = sigma ?? (address_of_word_labels ps label))
220           (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *)
221       | (* medium *)  #H1 #H2 #EQ %[@1] generalize in match H1; -H1;
222         generalize in match
223          (refl …
224            (split … 5 11 (sigma 〈preamble,instr_list〉 pol (address_of_word_labels_code_mem instr_list label))))
225         cases (split ????) in ⊢ (??%? → %) #fst_5_addr #rest_addr normalize nodelta; #EQ1
226         generalize in match
227          (refl …
228            (split … 5 11 (sigma 〈preamble,instr_list〉 pol (program_counter … ps))))
229         cases (split ????) in ⊢ (??%? → %) #fst_5_pc #rest_pc normalize nodelta; #EQ2
230         generalize in match (refl … (eq_bv … fst_5_addr fst_5_pc))
231         cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta; #EQ3 #TEQ [2: destruct (TEQ)]
232         generalize in match (option_destruct_Some ??? TEQ) -TEQ; #K1 >K1 in H2; whd in ⊢ (% → ?)
233         change in ⊢ (? →??%?) with (execute_1_0 ??)
234           cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
235           * * #H2a #H2b whd in ⊢ (% → ?) #H2c
236           >H2b >(eq_instruction_to_eq … H2a)
237           generalize in match EQ; -EQ;
238           whd in ⊢ (???% → ?);
239           #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) whd in ⊢ (??%?)
240           change with ((let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc) in ?)=?)
241           generalize in match (refl … (split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc)))
242           cases (split ????) in ⊢ (??%? → %) #pc_bu #pc_bl normalize nodelta; #EQ4
243           generalize in match (refl … (split bool 4 4 pc_bu))
244           cases (split ????) in ⊢ (??%? → %) #nu #nl normalize nodelta; #EQ5
245           generalize in match (refl … (split bool 3 8 rest_addr))
246           cases (split ????) in ⊢ (??%? → %) #relevant1 #relevant2 normalize nodelta; #EQ6
247           change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma … newppc) ? in ?) = ?)
248           generalize in match
249            (refl …
250             (half_add 16 (sigma 〈preamble,instr_list〉 pol newppc)
251             ((nu@@get_index' bool 0 3 nl:::relevant1)@@relevant2)))
252           cases (half_add ???) in ⊢ (??%? → %) #carry #new_pc normalize nodelta; #EQ7   
253           @split_eq_status try %
254            [ change with (? = sigma ?? (address_of_word_labels ps label))
255              (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *)
256            | whd in ⊢ (??%%) whd in ⊢ (??(?%?)?) whd in ⊢ (??(?(match ?(?%)? with [_ ⇒ ?])?)?)
257              @(bitvector_3_elim_prop … (\fst (split bool 3 8 rest_addr))) %]]
258  | (* Instruction *) -pi;  whd in ⊢ (? → ??%? → ?) *; normalize nodelta;
259    [1,2,3: (* ADD, ADDC, SUBB *) #arg1 #arg2 #MAP #H1 #H2 #EQ %[1,3,5:@1]
260       normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
261       change in ⊢ (? → ??%?) with (execute_1_0 ??)
262       cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
263       * * #H2a #H2b whd in ⊢ (% → ?) #H2c
264       >H2b >(eq_instruction_to_eq … H2a)
265       generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?); generalize in match MAP; -MAP;
266       @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1;
267       @(list_addressing_mode_tags_elim_prop … arg2) whd try % -arg2; #ARG2
268       normalize nodelta; #MAP;
269       [1: change in ⊢ (? → %) with
270        ((let 〈result,flags〉 ≝
271          add_8_with_carry
272           (get_arg_8 ? ps false ACC_A)
273           (get_arg_8 ?
274             (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps)))
275             false (DIRECT ARG2))
276           ? in ?) = ?)
277        [2,3: %]
278        change in ⊢ (???% → ?) with
279         (let 〈result,flags〉 ≝ add_8_with_carry ?(*(get_arg_8 ? ps false ACC_A)*) ?? in ?)
280        >get_arg_8_set_clock
281       [1,2: cases (addressing_mode_ok ???? ∧ addressing_mode_ok ????) in MAP ⊢ ?
282         [2,4: #abs @⊥ normalize in abs; destruct (abs)
283         |*:whd in ⊢ (??%? → ?) #H <(option_destruct_Some ??? H)]
284       [ change in ⊢ (? → %) with
285        ((let 〈result,flags〉 ≝
286          add_8_with_carry
287           (get_arg_8 ? ps false ACC_A)
288           (get_arg_8 ?
289             (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps)))
290             false (DIRECT ARG2))
291           ? in ?) = ?)
292          >get_arg_8_set_low_internal_ram
293       
294        cases (add_8_with_carry ???)
295         
296        [1,2,3,4,5,6,7,8: cases (add_8_with_carry ???) |*: cases (sub_8_with_carry ???)]
297       #result #flags
298       #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) %
299    | (* INC *) #arg1 #H1 #H2 #EQ %[@1]
300       normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?)
301       change in ⊢ (? → ??%?) with (execute_1_0 ??)
302       cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta;
303       * * #H2a #H2b whd in ⊢ (% → ?) #H2c
304       >H2b >(eq_instruction_to_eq … H2a)
305       generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?);
306       @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1; normalize nodelta; [1,2,3: #ARG]
307       [1,2,3,4: cases (half_add ???) #carry #result
308       | cases (half_add ???) #carry #bl normalize nodelta;
309         cases (full_add ????) #carry' #bu normalize nodelta ]
310        #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) -newppc';
311        [5: %
312        |1: <(set_arg_8_set_code_memory 0 [[direct]] ? ? ? (set_clock pseudo_assembly_program
313      (set_program_counter pseudo_assembly_program ps newppc)
314      (\fst  (ticks_of0 〈preamble,instr_list〉
315                   (program_counter pseudo_assembly_program ps)
316                   (Instruction (INC Identifier (DIRECT ARG))))
317       +clock pseudo_assembly_program
318        (set_program_counter pseudo_assembly_program ps newppc))) (load_code_memory assembled) result (DIRECT ARG))
319        [2,3: // ]
320            <(set_arg_8_set_program_counter 0 [[direct]] ? ? ? ? ?) [2://]
321            whd in ⊢ (??%%)
322            cases (split bool 4 4 ARG)
323            #nu' #nl'
324            normalize nodelta
325            cases (split bool 1 3 nu')
326            #bit_1' #ignore'
327            normalize nodelta
328            cases (get_index_v bool 4 nu' ? ?)
329            [ normalize nodelta (* HERE *) whd in ⊢ (??%%) %
330            |
331            ]
332cases daemon (* EASY CASES TO BE COMPLETED *)
333qed.
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