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Theorem btree-repl-dirty-address
⊦ ¬ adr1 ∈ alladrs ∧ r ∈ zh ∧ zh[r].dirty ∧ ((btree(rp, r, adr0, height, true, ri, iast, as, alladrs, nstat) * P))(zh) → ((btree(rp, r, adr1, height, true, ri, iast, as, (alladrs -- adr0) ++ adr1, nstat) * P))(zh)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 11
Used lemmas:
bleaf
,
maplet-null
,
btree
,
btree-dirty-adr-notin
,
btree-adrs
,
btree-refed-subseteq-alladrs
,
Used spec theorems:
set-union
/node-store/
del-in
Used simplifier rules:
znode
/
elim
set-basic
/node-store/
size-zero-01
maplet
/zheap/
map-in
znode
/
inj
maplet
/zheap/
at-eq
heap
/zheap/
nonnull
set-union
/node-store/
del-addeq-05
set-union
/node-store/
del-addin-01
heap-sep
/zheap/
trueH
heap-sep
/zheap/
true-and
heap-sep
/zheap/
true-rev
set-union
/node-store/
del-e-01
set-union
/node-store/
one-min
heap-sep
/zheap/
prop
heap-sep
/zheap/
and
heap-sep
/zheap/
and-com
heap-sep
/zheap/
and-ass
heap-sep
/zheap/
emp-sep
heap-sep
/zheap/
prop-shift
set-union
/node-store/
del-e-02
nat
/
ler
nat-basic
/
c
nat-basic
/
a
nat-basic
/
add-base
store+set
/index-store-address-store/
Dom
set-basic
/node-store/
ne-01
set-basic
/node-store/
sub-in
set-union
/node-store/
del-in
zbranch-array-ops
/
unmodified-dirty
heap-sep
/zheap/
sep-ass
heap-sep
/zheap/
sep-com
set-union
/node-store/
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