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Theorem btree-istore-reduce-refed
⊦ iast0 | as ⊆ iast1 ∧ ((btree(rp, rp0, adr, height, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) → ((btree(rp, rp0, adr, height, dirty, ri, iast1, as, alladrs, nstat) * P))(zh)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
btree-as-empty-rev
,
btree-inv-alloc
,
btree-inv-remove-refsize0
,
btree-istore-reduce
,
btree-istore-restrict-to-as
,
btree-restrict-union-proper
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 43
Used lemmas:
maplet-null
,
restrict-further
,
sep-forall-reduce
,
bnode
,
restrict-add-at
,
restrict-add-in
,
restrict-add-subseteq-at
,
restrict-add-subseteq-in
,
bleaf
,
btree
,
btree-adrs
,
btree-refed-subseteq-alladrs
,
Used spec theorems:
zbranch-array-ops
/
unmodified
set-union
/node-store/
delete-shift
Used simplifier rules:
set-basic
/node-store/
in-06
heap-sep
/zheap/
emp-sep
set-union
/node-store/
del-e-01
set-union
/node-store/
del-addeq-05
set-basic
/node-store/
sub-one-02
set-basic
/node-store/
ne
set-basic
/node-store/
size-one-01
set-basic
/node-store/
one-size
set-basic
/node-store/
in-04
set-union
/node-store/
del-e-02
znode
/
sel-04
nat-basic
/
succ
set-basic
/node-store/
size-zero-01
set-basic
/node-store/
ne-01
set-basic
/node-store/
sub-in
nat
/
elim-pred-c
constants
/
branchsize-0
nat-basic
/
f
nat
/
eqle-one
existential
/zheap/
exists-shift
nat
/
add-01
nat-basic
/
oz
nat
/
succ-01
nat
/
ler
nat-basic
/
lf-01
nat
/
fle-01
nat
/
lels
heap-sep
/zheap/
true-and
heap-sep
/zheap/
true-rev
heap-sep
/zheap/
prop
heap-sep
/zheap/
and
heap-sep
/zheap/
and-com
heap-sep
/zheap/
and-ass
heap-sep
/zheap/
prop-shift
nat-basic
/
add-base
zbranch
/
elim-01
zbranch
/
test-03
set-basic
/node-store/
subset-equal
set-basic
/node-store/
sub-ntrans
set-basic
/node-store/
in-03
set-basic
/node-store/
sub-add-03
address-set-array-ops
/
union-subset
nat
/
lez
nat-basic
/
a
nat-basic
/
c
nat-basic
/
s-04
store+set
/index-store-address-store/
Dom
set-basic
/node-store/
sub-add
nat
/
le-ls-simp
nat
/
lep-02
address-set-array-ops
/
subseteq-union-one-add
set-union
/node-store/
del-in
heap-sep
/zheap/
sep-ass
heap-sep
/zheap/
sep-com
zbranch-array-ops
/
unmodified-dirty
address-set-array-ops
/
subseteq-union-one