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Theorem gc-heap-free-h
⊦ n < m ∧ m ≤ # lpt ∧ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ ¬ n ∈ nx → gc-heap(lpt[n, mklp(m0, m1, LP_FREE, m2)], nx, m) = gc-heap(lpt, nx, m) -- key-index(n0, n)
Type: A user defined theorem
Validity: The proof is valid.
Features: ls, s,
Comment:
Used by:
gc-heap-free
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 15
Used lemmas:
gc-heap-in-h
,
gc-heap-write-above
,
gc-heap-rec
,
gc-heap-base
,
Used spec theorems:
Used simplifier rules:
nat
/
fle
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
/
ls-le-simp
elem-index
/gc-heap-base/
sel-01-M01
array
/lp-array/
Size-put
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
One
array
/lp-array/
cngetput
elem-index
/gc-heap-base/
sel-01-M03
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
size-zero-01
nat
/
lels
nat
/
lels-03
oelem
/nat-set/
irreflexivity
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-in-03
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-in
nat
/
anti
nat-basic
/
lf-02
array
/lp-array/
Put-same
lprops
/
inj
nat
/
ler
lprops
/
disj-01
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
une
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
una
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unc
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
uneq
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-addeq-05
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
del-e-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
sub-e
array
/lp-array/
Put-other
nat
/
lels-02
nat-basic
/
lf
nat-basic
/
f
nat-basic
/
succ
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
union-rem-unchdg
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
Delete
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
in-04
key-index
/gc-heap-rename-gc-heap-base/
inj