Changeset 1596

Timestamp:

Dec 7, 2011, 4:24:42 PM (8 years ago)

Author:

campbell

Message:

RTLabs structured traces: sort out passing of termination proofs around.

File:

• src/RTLabs/Traces.ma (modified) (3 diffs)

src/RTLabs/Traces.ma

@@ -243 +243 @@
 ] qed. 
 
-(*
-(* If we'll return then we must return from calls. *)
-lemma will_return_call : ∀ge,depth,s,trace.
-  will_return ge (S depth) s trace →
-  will_return ge depth s trace.
-#ge #depth #s #trace #H elim H in ⊢ ?;
-[ #s1 #tr #s2 #d1 #EX #tr1 #H1 #H2 #H3 #H4 /2/
-| #s1 #tr #s2 #d1 #EX #tr1 #H1 #H2 #H3 #H4 /2/
-| #H204 #H205 #H206 #H207 #H208 #H209 #H210 #H211 #H212 #H213 /2/
-| #H215 #H216 #H217 #H218 #H219 #H220 #H221
-  inversion H221
-  [ #H223 #H224 #H225 #H226 #H227 #H228 #H229 #H230 #H231 #H232 #H233 #H234 #H235 destruct >H220 in H229; * #E destruct
-  | #H237 #H238 #H239 #H240 #H241 #H242 #H243 #H244 #H245 #H246 #H247 #H248 #H249 destruct >H220 in H243; #E destruct
-  | #H265 #H266 #H267 #H268 #H269 #H270 #H271 #H272 #H273 #H274 #H275 #H276 #H277 destruct
-  | #H279 #H280 #H281 #H282 #H283 #H284 #H285 #H286 #H287 #H288 destruct
-] qed. check will_return_call.
-| #H130 #H131 #H132 #H133 #H134 #H135
-  inversion H
-  [ #H190 #H191 #H192 #H193 #H194 #H195 #H196 #H197 #H198 #H199 #H200 #H201 #H202 destruct
-    cases H196 #E destruct
-  
-
-let rec will_return_call ge depth s trace (H:will_return ge (S depth) s trace)
-  on H : will_return ge depth s trace ≝
-match H return λSdepth,s,trace. λ_. S depth = Sdepth → will_return ge depth s trace with
-[ wr_step s tr s' d EX trace CL H' ⇒ λE. wr_step ge s tr s' ? EX trace CL ?
-| wr_call s tr s' d EX trace CL H' ⇒ λE. ?
-| wr_ret s tr s' d EX trace CL H' ⇒ λE. ?
-| wr_base s tr s' EX trace CL ⇒ λE. ?
-] (refl ? (S depth)).
-[ @(match E return λx,E. will_return ? x ?? → will_return ge ??? with [ refl ⇒ λH''.? ] H')
-  @(will_return_call … H'')
-| *: cases daemon ] qed.
-| %2 /2/
-| destruct cases d in H' ⊢ %;
-  [ #H' @wr_base //
-  | #d' #H' %3 /2/
-  ]
-| destruct
-] qed.
-
-(* If we'll return then we must return from calls. *)
-lemma will_return_call : ∀ge,depth,s,trace.
-  will_return ge (S depth) s trace →
-  will_return ge depth s trace.
-#ge #depth #s #trace #H lapply (refl ? (S depth))
-generalize in ⊢ (???(?%) → ??%??); elim H in ⊢ (∀_.???% → %);
-[ #s1 #tr #s2 #d1 #EX #tr1 #H1 #H2 #H3 #n #H4 destruct %1 /2/
-| #s1 #tr #s2 #d1 #EX #tr1 #H1 #H2 #H3 #n #H4 destruct %2 /2/ @H3
-  
-discriminator nat.
-
-
-
-(* Find time until a nested call completes. *)
-lemma nth_is_return_down : ∀ge,n,depth,s,trace.
-  nth_is_return ge n (S depth) s trace →
-  ∃m. nth_is_return ge m depth s trace.
-#ge #n elim n
-(* It's impossible to run out of time... *)
-[ #depth #s #trace #H inversion H
-  [ #H11 #H12 #H13 #H14 #H15 #H16 #H17 #H18 #H19 #H20 #H21 #H22 #H23 #H24 #H25 destruct
-  | #H27 #H28 #H29 #H30 #H31 #H32 #H33 #H34 #H35 #H36 #H37 #H38 #H39 #H40 #H41 destruct
-  | #H43 #H44 #H45 #H46 #H47 #H48 #H49 #H50 #H51 #H52 #H53 #H54 #H55 #H56 #H57 destruct
-  | #H59 #H60 #H61 #H62 #H63 #H64 #H65 #H66 destruct
-  ]
-| #n' #IH #depth #s #trace #H inversion H
-  [ #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 #H1 #H2 #_ #E1 #E2 #E3 #E4 #E5 destruct
-    cases (IH depth s1' trace1 ?)
-    [ #m' #H' %{(S m')} %1 //
-    | //
-    ]
-  | #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 #H1 #H2 #_ #E1 #E2 #E3 #E4 #E5 destruct
-    cases (IH (S depth) s1' trace1 ?)
-    [ #m' #H' %{(S m')} %2 //
-    | //
-    ]
-  | #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 #H1 #H2 #_ #E1 #E2 #E3 #E4 #E5 destruct
-    cases (depth1) in H2 ⊢ %;
-    [ #H2 %{O} %4 //
-    | #depth' #H2 cases (IH depth' s1' trace1 ?)
-      [ #m' #H' %{(S m')} %3 //
-      | //
-      ]
-    ]
-  | #H68 #H69 #H70 #H71 #H72 #H73 #H74 #H75 destruct
-  ]
-] qed.
-
-lemma nth_is_return_call : ∀ge,n,s,tr,s',EX,trace.
-  RTLabs_classify s = cl_call →
-  nth_is_return ge n O s (ft_step ?? ge s tr s' EX trace) →
-  ∃m. nth_is_return ge m O s' trace.
-#ge #n #s #tr #s' #EX #trace #CLASS #H 
-inversion H
-[ #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 * #H1 #H2 #_ #E1 #E2 #E3 @⊥
-  -H2 destruct >H1 in CLASS; #E destruct
-| #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 #H1 #H2 #_ #E1 #E2 #E3 #E4 #E5 destruct
-  @nth_is_return_down //
-| #n1 #s1 #tr1 #s1' #depth1 #EX1 #trace1 #H1 #H2 #_ #E1 #E2 #E3 @⊥
-  -H2 destruct
-| #s1 #tr1 #s1' #EX1 #trace1 #E1 #E2 #E3 #E4 destruct @⊥ >E1 in CLASS; #E destruct
-] qed.
-
-lemma nth_is_return_notfn : ∀ge,n,s,tr,s',EX,trace.
+
+lemma will_return_notfn : ∀ge,d,s,tr,s',EX,trace.
   RTLabs_classify s = cl_other ∨ RTLabs_classify s = cl_jump →
-  nth_is_return ge n O s (ft_step ?? ge s tr s' EX trace) →
-  nth_is_return ge (pred n) O s' trace.
-#ge #n #s #tr #s' #EX #trace * #CL #TERM inversion TERM
-[ #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 #H14 #H15 destruct //
-| #H33 #H34 #H35 #H36 #H37 #H38 #H39 #H40 #H41 #H42 #H43 #H44 #H45 #H46 #H47 destruct >H40 in CL; #E destruct
-| #H49 #H50 #H51 #H52 #H53 #H54 #H55 #H56 #H57 #H58 #H59 #H60 #H61 #H62 #H63 destruct
-| #H65 #H66 #H67 #H68 #H69 #H70 #H71 #H72 #H73 #H74 #H75 destruct >H70 in CL; #E destruct
-| #H77 #H78 #H79 #H80 #H81 #H82 #H83 #H84 #H85 #H86 #H87 #H88 #H89 #H90 #H91 destruct //
-| #H93 #H94 #H95 #H96 #H97 #H98 #H99 #H100 #H101 #H102 #H103 #H104 #H105 #H106 #H107 destruct >H100 in CL; #E destruct
-| #H109 #H110 #H111 #H112 #H113 #H114 #H115 #H116 #H117 #H118 #H119 #H120 #H121 #H122 #H123 destruct
-| #H125 #H126 #H127 #H128 #H129 #H130 #H131 #H132 #H133 #H134 #H135 destruct >H130 in CL; #E destruct
-] qed.
-*)
-
-lemma will_return_notfn : ∀ge,s,tr,s',EX,trace.
-  RTLabs_classify s = cl_other ∨ RTLabs_classify s = cl_jump →
-  will_return ge O s (ft_step ?? ge s tr s' EX trace) →
-  will_return ge O s' trace.
-#ge #s #tr #s' #EX #trace * #CL #TERM inversion TERM
+  will_return ge d s (ft_step ?? ge s tr s' EX trace) →
+  will_return ge d s' trace.
+#ge #d #s #tr #s' #EX #trace * #CL #TERM inversion TERM
 [ #H290 #H291 #H292 #H293 #H294 #H295 #H296 #H297 #H298 #H299 #H300 #H301 #H302 destruct //
 | #H304 #H305 #H306 #H307 #H308 #H309 #H310 #H311 #H312 #H313 #H314 #H315 #H316 destruct >CL in H310; #E destruct
-| #H318 #H319 #H320 #H321 #H322 #H323 #H324 #H325 #H326 #H327 #H328 #H329 #H330 destruct
+| #H318 #H319 #H320 #H321 #H322 #H323 #H324 #H325 #H326 #H327 #H328 #H329 #H330 destruct >CL in H324; #E destruct
 | #H332 #H333 #H334 #H335 #H336 #H337 #H338 #H339 #H340 #H341 destruct >CL in H337; #E destruct
 | #H343 #H344 #H345 #H346 #H347 #H348 #H349 #H350 #H351 #H352 #H353 #H354 #H355 destruct //
 | #H357 #H358 #H359 #H360 #H361 #H362 #H363 #H364 #H365 #H366 #H367 #H368 #H369 destruct >CL in H363; #E destruct
-| #H371 #H372 #H373 #H374 #H375 #H376 #H377 #H378 #H379 #H380 #H381 #H382 #H383 destruct
+| #H371 #H372 #H373 #H374 #H375 #H376 #H377 #H378 #H379 #H380 #H381 #H382 #H383 destruct >CL in H377; #E destruct
 | #H385 #H386 #H387 #H388 #H389 #H390 #H391 #H392 #H393 #H394 destruct >CL in H390; #E destruct
 ] qed.
@@ -522 +403 @@
 (* Don't need to know that labels break loops because we have termination. *)
 
-record trace_result (ge:genv) (T:state → Type[0]) : Type[0] ≝ {
+(* A bit of mucking around with the depth to avoid proving termination after
+  termination. *)
+record trace_result (ge:genv) (depth:nat) (T:state → Type[0]) : Type[0] ≝ {
   new_state : state;
   remainder : flat_trace io_out io_in ge new_state;
   cost_labelled : well_cost_labelled_state new_state;
-  new_trace : T new_state
+  new_trace : T new_state;
+  terminates : match depth with
+               [ O ⇒ True
+               | S d ⇒ will_return ge d new_state remainder
+               ]
 }.
 
-record sub_trace_result (ge:genv) (T:trace_ends_with_ret → state → Type[0]) : Type[0] ≝ {
+record sub_trace_result (ge:genv) (depth:nat) (T:trace_ends_with_ret → state → Type[0]) : Type[0] ≝ {
   ends : trace_ends_with_ret;
-  trace_res :> trace_result ge (T ends);
-  terminates :
-    (* We handle returns specially *)
-    match ends with
-    [ doesnt_end_with_ret ⇒ will_return ge O (new_state ?? trace_res) (remainder ?? trace_res)
-    | ends_with_ret ⇒ True
-    ]
+  trace_res :> trace_result ge (match ends with [ doesnt_end_with_ret ⇒ S depth | _ ⇒ depth]) (T ends)
 }.
 
-definition replace_sub_trace : ∀ge,T1,T2.
-  ∀r:sub_trace_result ge T1. T2 (ends … r) (new_state … r) →sub_trace_result ge T2 ≝
-λge,T1,T2,r,trace.
-  mk_sub_trace_result ge T2
+definition replace_sub_trace : ∀ge,trm,T1,T2.
+  ∀r:sub_trace_result ge trm T1. T2 (ends … r) (new_state … r) → sub_trace_result ge trm T2 ≝
+λge,trm,T1,T2,r,trace.
+  mk_sub_trace_result ge trm T2
     (ends … r)
-    (mk_trace_result ge (T2 (ends … r))
+    (mk_trace_result ge ? (T2 (ends … r))
       (new_state … r)
       (remainder … r)
       (cost_labelled … r)
       trace
+      (terminates … r)
     )
-    (terminates … r)
 .
 
-definition replace_trace : ∀ge,T1,T2.
-  ∀r:trace_result ge T1. T2 (new_state … r) → trace_result ge T2 ≝
-λge,T1,T2,r,trace.
-  mk_trace_result ge T2
+definition replace_trace : ∀ge,trm,T1,T2.
+  ∀r:trace_result ge trm T1. T2 (new_state … r) → trace_result ge trm T2 ≝
+λge,trm,T1,T2,r,trace.
+  mk_trace_result ge trm T2
     (new_state … r)
     (remainder … r)
     (cost_labelled … r)
     trace
+    (terminates … r)
 .
 
-let rec make_label_return ge s
+let rec make_label_return ge depth s
   (trace: flat_trace io_out io_in ge s)
   (ENV_COSTLABELLED: well_cost_labelled_ge ge)
   (STATE_COSTLABELLED: well_cost_labelled_state s)  (* functions in the state *)
   (STATEMENT_COSTLABEL: RTLabs_cost s = true)       (* current statement is a cost label *)
-  (TERMINATES: will_return ge O s trace)
-  : trace_result ge (trace_label_return (RTLabs_status ge) s) ≝
-
-  let r ≝ make_label_label ge s trace ENV_COSTLABELLED STATE_COSTLABELLED STATEMENT_COSTLABEL TERMINATES in
-  match ends … r return λx. trace_label_label ? x ?? → match x with [doesnt_end_with_ret⇒ ?|_⇒ ?] → ? with
-  [ ends_with_ret ⇒ λtll,term.
-      replace_trace … r (tlr_base (RTLabs_status ge) s (new_state … r) tll)
-  | doesnt_end_with_ret ⇒ λtll,term.
-      let r' ≝ make_label_return ge (new_state … r)
-                 (remainder … r) ENV_COSTLABELLED (cost_labelled … r) ? term in
+  (TERMINATES: will_return ge depth s trace)
+  : trace_result ge depth (trace_label_return (RTLabs_status ge) s) ≝
+
+  let r ≝ make_label_label ge depth s trace ENV_COSTLABELLED STATE_COSTLABELLED STATEMENT_COSTLABEL TERMINATES in
+  match ends … r return λx. trace_result ge (match x with [ doesnt_end_with_ret ⇒ S depth | _ ⇒ depth]) (trace_label_label (RTLabs_status ge) x s) → ? with
+  [ ends_with_ret ⇒ λr.
+      replace_trace … r (tlr_base (RTLabs_status ge) s (new_state … r) (new_trace … r))
+  | doesnt_end_with_ret ⇒ λr.
+      let r' ≝ make_label_return ge depth (new_state … r)
+                 (remainder … r) ENV_COSTLABELLED (cost_labelled … r) ? (terminates ??? r) in
         replace_trace … r'
-          (tlr_step (RTLabs_status ge) s (new_state … r) (new_state … r') tll (new_trace … r'))
-  ] (new_trace … r) (terminates … r)
-
-and make_label_label ge s
+          (tlr_step (RTLabs_status ge) s (new_state … r) (new_state … r') (new_trace … r) (new_trace … r'))
+  ] (trace_res … r)
+
+and make_label_label ge depth s
   (trace: flat_trace io_out io_in ge s)
   (ENV_COSTLABELLED: well_cost_labelled_ge ge)
   (STATE_COSTLABELLED: well_cost_labelled_state s)  (* functions in the state *)
   (STATEMENT_COSTLABEL: RTLabs_cost s = true)       (* current statement is a cost label *)
-  (TERMINATES: will_return ge O s trace)
-  : sub_trace_result ge (λends. trace_label_label (RTLabs_status ge) ends s) ≝
-let r ≝ make_any_label ge s trace ENV_COSTLABELLED STATE_COSTLABELLED TERMINATES in
-  replace_sub_trace ??? r
+  (TERMINATES: will_return ge depth s trace)
+  : sub_trace_result ge depth (λends. trace_label_label (RTLabs_status ge) ends s) ≝
+let r ≝ make_any_label ge depth s trace ENV_COSTLABELLED STATE_COSTLABELLED TERMINATES in
+  replace_sub_trace … r
     (tll_base (RTLabs_status ge) (ends … r) s (new_state … r) (new_trace … r) STATEMENT_COSTLABEL)
 
-and make_any_label ge s
+and make_any_label ge depth s
   (trace: flat_trace io_out io_in ge s)
   (ENV_COSTLABELLED: well_cost_labelled_ge ge)
   (STATE_COSTLABELLED: well_cost_labelled_state s)  (* functions in the state *)
-  (TERMINATES: will_return ge O s trace)
-  : sub_trace_result ge (λends. trace_any_label (RTLabs_status ge) ends s) ≝
-match trace return λs,trace. well_cost_labelled_state s → will_return ??? trace → sub_trace_result ge (λends. trace_any_label (RTLabs_status ge) ends s) with
+  (TERMINATES: will_return ge depth s trace)
+  : sub_trace_result ge depth (λends. trace_any_label (RTLabs_status ge) ends s) ≝
+match trace return λs,trace. well_cost_labelled_state s → will_return ??? trace → sub_trace_result ge depth (λends. trace_any_label (RTLabs_status ge) ends s) with
 [ ft_stop st FINAL ⇒ λSTATE_COSTLABELLED,TERMINATES. ?
 | ft_step start tr next EV trace' ⇒ λSTATE_COSTLABELLED,TERMINATES.
@@ -607 +489 @@
         match RTLabs_cost next return λx. RTLabs_cost next = x → ? with
         [ true ⇒ λCS.
-            mk_sub_trace_result ge (λends. trace_any_label (RTLabs_status ge) ends start) doesnt_end_with_ret (mk_trace_result ge ? next trace' ? (tal_base_not_return (RTLabs_status ge) start next ???)) ?
+            mk_sub_trace_result ge depth (λends. trace_any_label (RTLabs_status ge) ends start)
+              doesnt_end_with_ret
+              (mk_trace_result ge ?? next trace' ? (tal_base_not_return (RTLabs_status ge) start next ???) ?)
         | false ⇒ λCS.
-            let r ≝ make_any_label ge next trace' ENV_COSTLABELLED ?? in
-                replace_sub_trace ??? r
+            let r ≝ make_any_label ge depth next trace' ENV_COSTLABELLED ?? in
+                replace_sub_trace … r
                   (tal_step_default (RTLabs_status ge) (ends … r) start next (new_state … r) ? (new_trace … r) ??)
         ] (refl ??)
     | cl_jump ⇒ λCL.
-        mk_sub_trace_result ge (λends. trace_any_label (RTLabs_status ge) ends start) doesnt_end_with_ret (mk_trace_result ge ? next trace' ? (tal_base_not_return (RTLabs_status ge) start next ???)) ?
+        mk_sub_trace_result ge depth (λends. trace_any_label (RTLabs_status ge) ends start)
+          doesnt_end_with_ret
+          (mk_trace_result ge ?? next trace' ? (tal_base_not_return (RTLabs_status ge) start next ???) ?) 
     | cl_call ⇒ λCL.
-        let r ≝ make_label_return ge next trace' ENV_COSTLABELLED ??? in
-        let r' ≝ make_any_label ge (new_state … r) (remainder … r) ENV_COSTLABELLED ?? in
-        replace_sub_trace ??? r'
+        let r ≝ make_label_return ge (S depth) next trace' ENV_COSTLABELLED ??? in
+        let r' ≝ make_any_label ge depth (new_state … r) (remainder … r) ENV_COSTLABELLED ?? in
+        replace_sub_trace ???? r'
           (tal_step_call (RTLabs_status ge) (ends … r') start next (new_state … r) (new_state … r') ? CL ? (new_trace … r) (new_trace … r'))
     | cl_return ⇒ λCL.
-        mk_sub_trace_result ge (λends. trace_any_label (RTLabs_status ge) ends start) ends_with_ret (mk_trace_result ge ? next trace' ? (tal_base_return (RTLabs_status ge) start next ? CL)) ?
+        mk_sub_trace_result ge depth (λends. trace_any_label (RTLabs_status ge) ends start)
+          ends_with_ret
+          (mk_trace_result ge ??
+            next
+            trace'
+            ?
+            (tal_base_return (RTLabs_status ge) start next ? CL)
+            ?)
     ] (refl ? (RTLabs_classify start))
 | ft_wrong start m EV ⇒ λSTATE_COSTLABELLED,TERMINATES. ⊥
 ] STATE_COSTLABELLED TERMINATES.
 
-[ @(trace_label_label_label … tll)
+[ @(trace_label_label_label … (new_trace … r))
 |
+| inversion TERMINATES
+  [ #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 -TERMINATES destruct >CL in H7; * #E destruct
+  | #H15 #H16 #H17 #H18 #H19 #H20 #H21 #H22 #H23 #H24 #H25 #H26 #H27 -TERMINATES destruct >CL in H21; #E destruct
+  | #H29 #H30 #H31 #H32 #H33 #H34 #H35 #H36 #H37 #H38 #H39 #H40 #H41 -TERMINATES destruct @H36
+  | #H43 #H44 #H45 #H46 #H47 #H48 #H49 #H50 #H51 #H52 whd @I
+  ]
 | %{tr} @EV
 | @(well_cost_labelled_state_step  … EV) //
-| @I
+| whd @(will_return_notfn … TERMINATES) %2 @CL
 | %{tr} @EV
 | % whd in ⊢ (% → ?); >CL #E destruct
 | @(well_cost_labelled_jump … EV) //
 | @(well_cost_labelled_state_step  … EV) //
-| @(will_return_notfn … TERMINATES) %2 @CL
 | (* oh dear *)
 | %{tr} @EV
 | @(cost_labelled … r)
-|
-|
-| 
-
- @(well_cost_labelled_state_step  … EV) //
+| @(terminates … r)
+| @(well_cost_labelled_state_step  … EV) //
+| @(well_cost_labelled_call … EV) //
+| inversion TERMINATES
+  [ #H54 #H55 #H56 #H57 #H58 #H59 #H60 #H61 #H62 #H63 #H64 #H65 #H66 -TERMINATES destruct >CL in H60; * #E destruct
+  | #H68 #H69 #H70 #H71 #H72 #H73 #H74 #H75 #H76 #H77 #H78 #H79 #H80 -TERMINATES destruct @H75
+  | #H82 #H83 #H84 #H85 #H86 #H87 #H88 #H89 #H90 #H91 #H92 #H93 #H94 -TERMINATES destruct >CL in H88; #E destruct
+  | #H96 #H97 #H98 #H99 #H100 #H101 #H102 #H103 #H104 #H105 -TERMINATES destruct >CL in H101; #E destruct
+  ]
+| whd @(will_return_notfn … TERMINATES) %1 @CL
+| %{tr} @EV
 | % whd in ⊢ (% → ?); >CL #E destruct
 | @CS
-| @(nth_is_return_notfn … TERMINATES) %1 @CL
+| @(well_cost_labelled_state_step  … EV) //
 | % whd in ⊢ (% → ?); >CS #E destruct
 | @CL
 | %{tr} @EV
 | @(well_cost_labelled_state_step  … EV) //
-| @(nth_is_return_notfn … TERMINATES) %1 @CL
+| @(will_return_notfn … TERMINATES) %1 @CL
 | inversion TERMINATES
-  [ #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 #H14 #H15 -TERMINATES destruct
-  | #H17 #H18 #H19 #H20 #H21 #H22 #H23 #H24 #H25 #H26 #H27 #H28 #H29 #H30 #H31 -TERMINATES destruct
-  | #H33 #H34 #H35 #H36 #H37 #H38 #H39 #H40 #H41 #H42 #H43 #H44 #H45 #H46 #H47 -TERMINATES destruct
-  | #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 -TERMINATES destruct
+  [ #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 -TERMINATES destruct
+  | #H17 #H18 #H19 #H20 #H21 #H22 #H23 #H24 #H25 #H26 #H27 #H28 #H29 -TERMINATES destruct
+  | #H33 #H34 #H35 #H36 #H37 #H38 #H39 #H40 #H41 #H42 #H43 #H44 #H45 -TERMINATES destruct
+  | #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 -TERMINATES destruct
   ]
 |