source: src/ASM/AssemblyProof.ma @ 849

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1include "ASM/Assembly.ma".
2include "ASM/Interpret.ma".
3
4(* RUSSEL **)
5
6include "basics/jmeq.ma".
7
8definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p.
9definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w].
10
11coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?.
12coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?.
13
14axiom VOID: Type[0].
15axiom assert_false: VOID.
16definition bigbang: ∀A:Type[0].False → VOID → A.
17 #A #abs cases abs
18qed.
19
20coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.
21
22lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p).
23 #A #P #p cases p #w #q @q
24qed.
25
26(* END RUSSELL **)
27
28(* This establishes the correspondence between pseudo program counters and
29   program counters. It is at the heart of the proof. *)
30(*CSC: code taken from build_maps *)
31definition sigma0: pseudo_assembly_program → option (nat × (nat × (BitVectorTrie Word 16))) ≝
32 λinstr_list.
33  foldl ??
34    (λt. λi.
35       match t with
36       [ None ⇒ None ?
37       | Some ppc_pc_map ⇒
38         let 〈ppc,pc_map〉 ≝ ppc_pc_map in
39         let 〈program_counter, sigma_map〉 ≝ pc_map in
40         let 〈label, i〉 ≝ i in
41          match construct_costs instr_list program_counter (λx. zero ?) (λx. zero ?) (Stub …) i with
42           [ None ⇒ None ?
43           | Some pc_ignore ⇒
44              let 〈pc,ignore〉 ≝ pc_ignore in
45              Some … 〈S ppc,〈pc, insert ? ? (bitvector_of_nat ? ppc) (bitvector_of_nat ? pc) sigma_map〉〉 ]
46       ]) (Some ? 〈0, 〈0, (Stub ? ?)〉〉) (\snd instr_list).
47       
48definition tech_pc_sigma0: pseudo_assembly_program → option nat ≝
49 λinstr_list.
50  match sigma0 instr_list with
51   [ None ⇒ None …
52   | Some result ⇒
53      let 〈ppc,pc_sigma_map〉 ≝ result in
54      let 〈pc, sigma_map〉 ≝ pc_sigma_map in
55       Some … pc ].
56
57definition sigma_safe: pseudo_assembly_program → option (Word → Word) ≝       
58 λinstr_list.
59  match sigma0 instr_list with
60  [ None ⇒ None ?
61  | Some result ⇒
62    let 〈ppc,pc_sigma_map〉 ≝ result in
63    let 〈pc, sigma_map〉 ≝ pc_sigma_map in
64      if gtb pc (2^16) then
65        None ?
66      else
67        Some ? (λx.lookup ?? x sigma_map (zero …)) ].
68
69axiom policy_ok: ∀p. sigma_safe p ≠ None ….
70
71definition sigma: pseudo_assembly_program → Word → Word ≝
72 λp.
73  match sigma_safe p return λr:option (Word → Word). r ≠ None … → Word → Word with
74   [ None ⇒ λabs. ⊥
75   | Some r ⇒ λ_.r] (policy_ok p).
76 cases abs //
77qed.
78
79(*
80definition build_maps' ≝
81  λpseudo_program.
82  let 〈preamble,instr_list〉 ≝ pseudo_program in
83  let result ≝
84   foldl
85    ((BitVectorTrie Word 16) × (nat × (BitVectorTrie Word 16)))
86    (option Identifier × pseudo_instruction)
87    (λt,i.
88      let 〈labels, pc_costs〉 ≝ t in
89      let 〈program_counter, costs〉 ≝ pc_costs in
90       let 〈label, i'〉 ≝ i in
91       let labels ≝
92         match label with
93         [ None ⇒ labels
94         | Some label ⇒
95           let program_counter_bv ≝ bitvector_of_nat ? program_counter in
96             insert ? ? label program_counter_bv labels
97         ]
98       in
99         match construct_costs pseudo_program program_counter (λx. zero ?) (λx. zero ?) costs i' with
100         [ None ⇒
101            let dummy ≝ 〈labels,pc_costs〉 in
102             dummy
103         | Some construct ⇒ 〈labels, construct〉
104         ]
105    ) 〈(Stub ? ?), 〈0, (Stub ? ?)〉〉 instr_list
106  in
107   let 〈labels, pc_costs〉 ≝ result in
108   let 〈pc, costs〉 ≝ pc_costs in
109    〈labels, costs〉.
110
111(*
112notation < "hvbox('let' 〈ident x,ident y〉 ≝ t 'in' s)"
113 with precedence 10
114for @{ match $t with [ pair ${ident x} ${ident y} ⇒ $s ] }.
115*)
116
117lemma build_maps_ok:
118 ∀p:pseudo_assembly_program.
119  let 〈labels,costs〉 ≝ build_maps' p in
120   ∀pc.
121    (nat_of_bitvector … pc) < length … (\snd p) →
122     lookup ?? pc labels (zero …) = sigma p (\snd (fetch_pseudo_instruction (\snd p) pc)).
123 #p cases p #preamble #instr_list
124  elim instr_list
125   [ whd #pc #abs normalize in abs; cases (not_le_Sn_O ?) [#H cases (H abs) ]
126   | #hd #tl #IH
127    whd in ⊢ (match % with [ _ ⇒ ?])
128   ]
129qed.
130*)
131
132(*
133lemma list_elim_rev:
134 ∀A:Type[0].∀P:list A → Prop.
135  P [ ] → (∀n,l. length l = n → P l → 
136  P [ ] → (∀l,a. P l → P (l@[a])) →
137   ∀l. P l.
138 #A #P
139qed.*)
140
141lemma length_append:
142 ∀A.∀l1,l2:list A.
143  |l1 @ l2| = |l1| + |l2|.
144 #A #l1 elim l1
145  [ //
146  | #hd #tl #IH #l2 normalize <IH //]
147qed.
148
149lemma rev_preserves_length:
150 ∀A.∀l. length … (rev A l) = length … l.
151  #A #l elim l
152   [ %
153   | #hd #tl #IH normalize >length_append normalize /2/ ]
154qed.
155
156lemma rev_append:
157 ∀A.∀l1,l2.
158  rev A (l1@l2) = rev A l2 @ rev A l1.
159 #A #l1 elim l1 normalize //
160qed.
161 
162lemma rev_rev: ∀A.∀l. rev … (rev A l) = l.
163 #A #l elim l
164  [ //
165  | #hd #tl #IH normalize >rev_append normalize // ]
166qed.
167
168lemma split_len_Sn:
169 ∀A:Type[0].∀l:list A.∀len.
170  length … l = S len →
171   Σl'.Σa. l = l'@[a] ∧ length … l' = len.
172 #A #l elim l
173  [ normalize #len #abs destruct
174  | #hd #tl #IH #len
175    generalize in match (rev_rev … tl)
176    cases (rev A tl) in ⊢ (??%? → ?)
177     [ #H <H normalize #EQ % [@[ ]] % [@hd] normalize /2/ 
178     | #a #l' #H <H normalize #EQ
179      %[@(hd::rev … l')] %[@a] % //
180      >length_append in EQ #EQ normalize in EQ; normalize;
181      generalize in match (injective_S … EQ) #EQ2 /2/ ]]
182qed.
183
184lemma list_elim_rev:
185 ∀A:Type[0].∀P:list A → Type[0].
186  P [ ] → (∀l,a. P l → P (l@[a])) →
187   ∀l. P l.
188 #A #P #H1 #H2 #l
189 generalize in match (refl … (length … l))
190 generalize in ⊢ (???% → ?) #n generalize in match l
191 elim n
192  [ #L cases L [ // | #x #w #abs (normalize in abs) @⊥ // ]
193  | #m #IH #L #EQ
194    cases (split_len_Sn … EQ) #l' * #a * /3/ ]
195qed.
196
197axiom is_prefix: ∀A:Type[0]. list A → list A → Prop.
198axiom prefix_of_append:
199 ∀A:Type[0].∀l,l1,l2:list A.
200  is_prefix … l l1 → is_prefix … l (l1@l2).
201
202record Propify (A:Type[0]) : Prop ≝ { in_propify: A }.
203
204definition Propify_elim: ∀A. ∀P:Prop. (A → P) → (Propify A → P) ≝
205 λA,P,H,x. match x with [ mk_Propify p ⇒ H p ].
206
207let rec foldli (A: Type[0]) (B: Type[0]) (f: Propify nat → A → B → A) (i: Propify nat) (a: A) (l: list B) on l ≝
208  match l with
209  [ nil ⇒ a
210  | cons hd tl ⇒ foldli A B f (match i with [ mk_Propify i ⇒ mk_Propify … (S i)]) (f i a hd) tl
211  ].
212
213definition build_maps' ≝
214  λpseudo_program.
215  let 〈preamble,instr_list〉 ≝ pseudo_program in
216  let result ≝
217   foldl
218    (Σt:((BitVectorTrie Word 16) × (nat × (BitVectorTrie Word 16))).
219          ∃instr_list_prefix. is_prefix ? instr_list_prefix instr_list ∧
220           tech_pc_sigma0 〈preamble,instr_list_prefix〉 = Some ? (\fst (\snd t)))
221    (Σi:option Identifier × pseudo_instruction. ∀instr_list_prefix.
222          let instr_list_prefix' ≝ instr_list_prefix @ [i] in
223           is_prefix ? instr_list_prefix' instr_list →
224           tech_pc_sigma0 〈preamble,instr_list_prefix'〉 ≠ None ?)
225    (λt: Σt:((BitVectorTrie Word 16) × (nat × (BitVectorTrie Word 16))).
226          ∃instr_list_prefix. is_prefix ? instr_list_prefix instr_list ∧
227           tech_pc_sigma0 〈preamble,instr_list_prefix〉 = Some ? (\fst (\snd t)).
228     λi: Σi:option Identifier × pseudo_instruction. ∀instr_list_prefix.
229          let instr_list_prefix' ≝ instr_list_prefix @ [i] in
230           is_prefix ? instr_list_prefix' instr_list →
231           tech_pc_sigma0 〈preamble,instr_list_prefix'〉 ≠ None ? .
232      let 〈labels, pc_costs〉 ≝ t in
233      let 〈program_counter, costs〉 ≝ pc_costs in
234       let 〈label, i'〉 ≝ i in
235       let labels ≝
236         match label with
237         [ None ⇒ labels
238         | Some label ⇒
239           let program_counter_bv ≝ bitvector_of_nat ? program_counter in
240             insert ? ? label program_counter_bv labels
241         ]
242       in
243         match construct_costs pseudo_program program_counter (λx. zero ?) (λx. zero ?) costs i' with
244         [ None ⇒
245            let dummy ≝ 〈labels,pc_costs〉 in
246              dummy
247         | Some construct ⇒ 〈labels, construct〉
248         ]
249    ) 〈(Stub ? ?), 〈0, (Stub ? ?)〉〉 ?(*instr_list*)
250  in
251   let 〈labels, pc_costs〉 ≝ result in
252   let 〈pc, costs〉 ≝ pc_costs in
253    〈labels, costs〉.
254 [4: @(list_elim_rev ?
255       (λinstr_list. list (
256        (Σi:option Identifier × pseudo_instruction. ∀instr_list_prefix.
257          let instr_list_prefix' ≝ instr_list_prefix @ [i] in
258           is_prefix ? instr_list_prefix' instr_list →
259           tech_pc_sigma0 〈preamble,instr_list_prefix'〉 ≠ None ?)))
260       ?? instr_list) (* CSC: BAD ORDER FOR CODE EXTRACTION *)
261      [ @[ ]
262      | #l' #a #limage %2
263        [ %[@a] #PREFIX #PREFIX_OK
264        | (* CSC: EVEN WORST CODE FOR EXTRACTION: WE SHOULD STRENGTHEN
265             THE INDUCTION HYPOTHESIS INSTEAD *)
266          elim limage
267           [ %1
268           | #HD #TL #IH @(?::IH) cases HD #ELEM #K1 %[@ELEM] #K2 #K3
269             @K1 @(prefix_of_append ???? K3)
270           ] 
271        ]
272       
273       
274     
275 
276  cases t in c2 ⊢ % #t' * #LIST_PREFIX * #H1t' #H2t' #HJMt'
277     % [@ (LIST_PREFIX @ [i])] %
278      [ cases (sig2 … i LIST_PREFIX) #K1 #K2 @K1
279      | (* DOABLE IN PRINCIPLE *)
280      ]
281 | (* assert false case *)
282 |3: % [@ ([ ])] % [2: % | (* DOABLE *)]
283 |   
284
285let rec encoding_check (code_memory: BitVectorTrie Byte 16) (pc: Word) (final_pc: Word)
286                       (encoding: list Byte) on encoding: Prop ≝
287  match encoding with
288  [ nil ⇒ final_pc = pc
289  | cons hd tl ⇒
290    let 〈new_pc, byte〉 ≝ next code_memory pc in
291      hd = byte ∧ encoding_check code_memory new_pc final_pc tl
292  ].
293
294definition assembly_specification:
295  ∀assembly_program: pseudo_assembly_program.
296  ∀code_mem: BitVectorTrie Byte 16. Prop ≝
297  λpseudo_assembly_program.
298  λcode_mem.
299    ∀pc: Word.
300      let 〈preamble, instr_list〉 ≝ pseudo_assembly_program in
301      let 〈pre_instr, pre_new_pc〉 ≝ fetch_pseudo_instruction instr_list pc in
302      let labels ≝ λx. sigma' pseudo_assembly_program (address_of_word_labels_code_mem instr_list x) in
303      let datalabels ≝ λx. sigma' pseudo_assembly_program (lookup ? ? x (construct_datalabels preamble) (zero ?)) in
304      let pre_assembled ≝ assembly_1_pseudoinstruction pseudo_assembly_program
305       (sigma' pseudo_assembly_program pc) labels datalabels pre_instr in
306      match pre_assembled with
307       [ None ⇒ True
308       | Some pc_code ⇒
309          let 〈new_pc,code〉 ≝ pc_code in
310           encoding_check code_mem pc (sigma' pseudo_assembly_program pre_new_pc) code ].
311
312axiom assembly_meets_specification:
313  ∀pseudo_assembly_program.
314    match assembly pseudo_assembly_program with
315    [ None ⇒ True
316    | Some code_mem_cost ⇒
317      let 〈code_mem, cost〉 ≝ code_mem_cost in
318        assembly_specification pseudo_assembly_program (load_code_memory code_mem)
319    ].
320(*
321  # PROGRAM
322  [ cases PROGRAM
323    # PREAMBLE
324    # INSTR_LIST
325    elim INSTR_LIST
326    [ whd
327      whd in ⊢ (∀_. %)
328      # PC
329      whd
330    | # INSTR
331      # INSTR_LIST_TL
332      # H
333      whd
334      whd in ⊢ (match % with [ _ ⇒ ? | _ ⇒ ?])
335    ]
336  | cases not_implemented
337  ] *)
338
339definition status_of_pseudo_status: PseudoStatus → option Status ≝
340 λps.
341  let pap ≝ code_memory … ps in
342   match assembly pap with
343    [ None ⇒ None …
344    | Some p ⇒
345       let cm ≝ load_code_memory (\fst p) in
346       let pc ≝ sigma' pap (program_counter ? ps) in
347        Some …
348         (mk_PreStatus (BitVectorTrie Byte 16)
349           cm
350           (low_internal_ram … ps)
351           (high_internal_ram … ps)
352           (external_ram … ps)
353           pc
354           (special_function_registers_8051 … ps)
355           (special_function_registers_8052 … ps)
356           (p1_latch … ps)
357           (p3_latch … ps)
358           (clock … ps)) ].
359
360definition write_at_stack_pointer':
361 ∀M. ∀ps: PreStatus M. Byte → Σps':PreStatus M.(code_memory … ps = code_memory … ps') ≝
362  λM: Type[0].
363  λs: PreStatus M.
364  λv: Byte.
365    let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in
366    let bit_zero ≝ get_index_v… nu O ? in
367    let bit_1 ≝ get_index_v… nu 1 ? in
368    let bit_2 ≝ get_index_v… nu 2 ? in
369    let bit_3 ≝ get_index_v… nu 3 ? in
370      if bit_zero then
371        let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
372                              v (low_internal_ram ? s) in
373          set_low_internal_ram ? s memory
374      else
375        let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
376                              v (high_internal_ram ? s) in
377          set_high_internal_ram ? s memory.
378  [ cases l0 %
379  |2,3,4,5: normalize repeat (@ le_S_S) @ le_O_n ]
380qed.
381
382definition execute_1_pseudo_instruction': (Word → nat) → ∀ps:PseudoStatus.
383 Σps':PseudoStatus.(code_memory … ps = code_memory … ps')
384
385  λticks_of.
386  λs.
387  let 〈instr, pc〉 ≝ fetch_pseudo_instruction (\snd (code_memory ? s)) (program_counter ? s) in
388  let ticks ≝ ticks_of (program_counter ? s) in
389  let s ≝ set_clock ? s (clock ? s + ticks) in
390  let s ≝ set_program_counter ? s pc in
391    match instr with
392    [ Instruction instr ⇒
393       execute_1_preinstruction … (λx, y. address_of_word_labels y x) instr s
394    | Comment cmt ⇒ s
395    | Cost cst ⇒ s
396    | Jmp jmp ⇒ set_program_counter ? s (address_of_word_labels s jmp)
397    | Call call ⇒
398      let a ≝ address_of_word_labels s call in
399      let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr ? s SFR_SP) (bitvector_of_nat 8 1) in
400      let s ≝ set_8051_sfr ? s SFR_SP new_sp in
401      let 〈pc_bu, pc_bl〉 ≝ split ? 8 8 (program_counter ? s) in
402      let s ≝ write_at_stack_pointer' ? s pc_bl in
403      let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr ? s SFR_SP) (bitvector_of_nat 8 1) in
404      let s ≝ set_8051_sfr ? s SFR_SP new_sp in
405      let s ≝ write_at_stack_pointer' ? s pc_bu in
406        set_program_counter ? s a
407    | Mov dptr ident ⇒
408       set_arg_16 ? s (get_arg_16 ? s (DATA16 (address_of_word_labels s ident))) dptr
409    ].
410 [
411 |2,3,4: %
412 | <(sig2 … l7) whd in ⊢ (??? (??%)) <(sig2 … l5) %
413 |
414 | %
415 ]
416 cases not_implemented
417qed.
418
419(*
420lemma execute_code_memory_unchanged:
421 ∀ticks_of,ps. code_memory ? ps = code_memory ? (execute_1_pseudo_instruction ticks_of ps).
422 #ticks #ps whd in ⊢ (??? (??%))
423 cases (fetch_pseudo_instruction (\snd (code_memory pseudo_assembly_program ps))
424  (program_counter pseudo_assembly_program ps)) #instr #pc
425 whd in ⊢ (??? (??%)) cases instr
426  [ #pre cases pre
427     [ #a1 #a2 whd in ⊢ (??? (??%)) cases (add_8_with_carry ???) #y1 #y2 whd in ⊢ (??? (??%))
428       cases (split ????) #z1 #z2 %
429     | #a1 #a2 whd in ⊢ (??? (??%)) cases (add_8_with_carry ???) #y1 #y2 whd in ⊢ (??? (??%))
430       cases (split ????) #z1 #z2 %
431     | #a1 #a2 whd in ⊢ (??? (??%)) cases (sub_8_with_carry ???) #y1 #y2 whd in ⊢ (??? (??%))
432       cases (split ????) #z1 #z2 %
433     | #a1 whd in ⊢ (??? (??%)) cases a1 #x #H whd in ⊢ (??? (??%)) cases x
434       [ #x1 whd in ⊢ (??? (??%))
435     | *: cases not_implemented
436     ]
437  | #comment %
438  | #cost %
439  | #label %
440  | #label whd in ⊢ (??? (??%)) cases (half_add ???) #x1 #x2 whd in ⊢ (??? (??%))
441    cases (split ????) #y1 #y2 whd in ⊢ (??? (??%)) cases (half_add ???) #z1 #z2
442    whd in ⊢ (??? (??%)) whd in ⊢ (??? (??%)) cases (split ????) #w1 #w2
443    whd in ⊢ (??? (??%)) cases (get_index_v bool ????) whd in ⊢ (??? (??%))
444    (* CSC: ??? *)
445  | #dptr #label (* CSC: ??? *)
446  ]
447  cases not_implemented
448qed.
449*)
450
451lemma status_of_pseudo_status_failure_depends_only_on_code_memory:
452 ∀ps,ps': PseudoStatus.
453  code_memory … ps = code_memory … ps' →
454   match status_of_pseudo_status ps with
455    [ None ⇒ status_of_pseudo_status ps' = None …
456    | Some _ ⇒ ∃w. status_of_pseudo_status ps' = Some … w
457    ].
458 #ps #ps' #H whd in ⊢ (mat
459 ch % with [ _ ⇒ ? | _ ⇒ ? ])
460 generalize in match (refl … (assembly (code_memory … ps)))
461 cases (assembly ?) in ⊢ (???% → %)
462  [ #K whd whd in ⊢ (??%?) <H >K %
463  | #x #K whd whd in ⊢ (?? (λ_.??%?)) <H >K % [2: % ] ]
464qed.*)
465
466let rec encoding_check' (code_memory: BitVectorTrie Byte 16) (pc: Word) (encoding: list Byte) on encoding: Prop ≝
467  match encoding with
468  [ nil ⇒ True
469  | cons hd tl ⇒
470    let 〈new_pc, byte〉 ≝ next code_memory pc in
471      hd = byte ∧ encoding_check' code_memory new_pc tl
472  ].
473
474lemma test:
475  ∀i: instruction.
476  ∃pc.
477  let assembled ≝ assembly1 i in
478  let code_memory ≝ load_code_memory assembled in
479  let fetched ≝ fetch code_memory pc in
480  let 〈instr_pc, ticks〉 ≝ fetched in
481    \fst instr_pc = i.
482  # INSTR
483  %
484  [ @ (zero 16)
485  | cases INSTR
486  ].
487
488lemma test:
489  ∀pc: Word.
490  ∀code_memory: BitVectorTrie Byte 16.
491  ∀i: instruction.
492    let assembled ≝ assembly1 i in
493      encoding_check' code_memory pc assembled →
494        let 〈instr_pc, ignore〉 ≝ fetch code_memory pc in
495        let 〈instr, pc〉 ≝ instr_pc in
496          instr = i.
497  # PC # CODE_MEMORY # INSTRUCTION
498  whd
499  whd in ⊢ (? → match % with [ _ ⇒ ? ])
500  cases (next CODE_MEMORY PC)
501  whd
502  # PC1 # V1
503
504
505  cases (fetch CODE_MEMORY PC)
506  # INSTR_PC
507  # TICKS
508  cases (INSTRUCTION)
509  [ # ADDR11
510    # ENCODING_CHECK
511    whd in ENCODING_CHECK;
512    normalize
513    cases (INSTR_PC)
514    # INSTR
515    # PC
516    normalize
517   
518   
519  # ENCODING
520  normalize
521  [ cases INSTR_PC
522    # NEW_INSTRUCTION
523    # PC
524    normalize
525    normalize in ENCODING;
526  | # ASSEMBLED
527    whd
528 
529lemma main_thm:
530 ∀ticks_of.
531 ∀ps: PseudoStatus.
532  match status_of_pseudo_status ps with [ None ⇒ True | Some s ⇒
533  let ps' ≝ execute_1_pseudo_instruction ticks_of ps in
534  match status_of_pseudo_status ps' with [ None ⇒ True | Some s'' ⇒
535  let s' ≝ execute_1 s in
536   s = s'']].
537 #ticks_of #ps
538 whd in ⊢ (match % with [ _ ⇒ ? | _ ⇒ ? ])
539 cases (assembly (code_memory pseudo_assembly_program ps)) [%] * #cm #costs whd
540 whd in ⊢ (match % with [ _ ⇒ ? | _ ⇒ ? ])
541 generalize in match (sig2 … (execute_1_pseudo_instruction' ticks_of ps))
542 
543 cases (status_of_pseudo_status (execute_1_pseudo_instruction ticks_of ps)) [%] #s'' whd
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