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Theorem gc-heap-in-h
⊦ n ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bin-heap-inv-write-other
,
gc-heap-append-log-h
,
gc-heap-free-h
,
gc-heap-in
,
gc-heap-update-h
,
Used by units in proved state:
persistence-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 11
Used lemmas:
gc-heap-rec
,
gc-heap-base
,
Used spec theorems:
Used simplifier rules:
lprops
/
elim
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
In-empty
nat-basic
/
zero-01
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
One
nat
/
succ-01
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
nat-basic
/
ls-02
oelem
/nat-set/
ls-le
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unin-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/
unin
nat
/
lels
nat
/
anti
nat
/
fle-01
nat
/
ler
lprops
/
inj
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
in-04
key-index
/gc-heap-rename-gc-heap-base/
inj
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne
nat-basic
/
lf-02
nat-basic
/
lf-01
nat-basic
/
f
oelem
/nat-set/
irreflexivity
nat
/
lels-03
nat-basic
/
lf
nat-basic
/
succ