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Theorem gc-heap-update-h
⊦ n < m ∧ m ≤ # lpt ∧ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ ¬ n ∈ nx → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m) = (gc-heap(lpt, nx, m) -- key-index(n0, n)) ++ key-index(m0, n)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
gc-heap-update
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 21
Used lemmas:
gc-heap-in-h
,
gc-heap-write-above
,
gc-heap-rec
,
gc-heap-base
,
Used spec theorems:
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ext-rec
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unrax
Used simplifier rules:
nat
/
fle
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne
nat
/
lez
nat-basic
/
zero-01
nat-basic
/
s-04
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
undel-02
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
lprops
/
elim
nat
/
lels
nat
/
ls-le-simp
array
/lp-array/
Size-put
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
One
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-addeq-05
nat
/
ler
array
/lp-array/
Put-same
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
size-zero-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
in-02
nat
/
lels-03
oelem
/nat-set/
irreflexivity
nat-basic
/
succ
lprops
/
inj
nat-basic
/
lf
nat-basic
/
f
nat
/
lels-02
array
/lp-array/
Put-other
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-e-01
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unc
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
una
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
une
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unadd
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
In-insert
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
Delete
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
in-04
key-index
/gc-heap-rename-gc-heap-base/
inj