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Theorem valid-wl-next-free
m < # apebs, # apebs = # wlar ⊦ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false) → valid-wl(subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m0, free)], 0, m + 1))
Type: A user defined theorem
Validity: The proof is valid.
Features: ss,
Comment:
Used by:
Used by units in proved state:
ubi-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 0
Proof steps: 31
Used lemmas:
ls-at-subarray-pebs
,
ls-at-subarray-wlar
,
valid-wl
,
Used spec theorems:
Used simplifier rules:
bag-union
/nat-bag/
union-com
bag-union
/nat-bag/
union-ass
bag-union
/nat-bag/
union-empty
sqns
/
valid-sqns-rec
nat
/
le-ls-simp
nat
/
succ-01
array
/wlarray-base/
Size-put
sqns
/
valid-sqns-subarray
array-copy
/wlarray-base/
subarray-at
nat-basic
/
add-base
array-copy
/apebs/
subarray-at
nat-basic
/
ls-02
oelem
/nat-set/
transitivity
nat-basic
/
lf-02
nat
/
fle-01
nat
/
lels
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
nat
/
le-def
array-copy
/wlarray-base/
size-subarray
apeb
/
elim
array
/wlarray-base/
cngetput
wlentry
/
elim-02
array
/wlarray-base/
Put-same
wlentry
/
inj-03
nat
/
ler
valid-peb
/
valid-peb-vidhdr-empty
apeb
/
inj
nat-basic
/
lf-01
nat-basic
/
succ
nat-basic
/
lf
nat-basic
/
f
nat
/
lels-02
array
/wlarray-base/
Put-other
wlstatus
/
disj-06
wlstatus
/
disj-04
wlstatus
/
disj-05
wlstatus
/
disj-02
wlstatus
/
disj-03
aecheader
/
inj
wlstatus
/
disj-01
valid-peb
/
valid-peb-unique
wlentry
/
sel-04
apeb
/
sel-08
apeb
/
sel-05
apeb
/
sel-04
wlentry
/
sel-05