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Theorem btree-clean-fwd
⊦ ((btree(rp0, r0, adr, height0, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0) ∧ ((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1) → height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1
Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by:
btree-inv-clean-commit
,
btree-inv-crash
,
btree-inv-root-null
,
btree-inv-root-null-or-clean
,
btree-ri-unique
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 27
Proof steps: 69
Used lemmas:
btree-remove-context
,
nat-le-eq
,
ri-range-ext
,
bnode
,
bleaf
,
btree
,
btree-leaf-adr
,
btree-adrs
,
btree-refed-subseteq-alladrs
,
btree-clean-alladrs
,
Used spec theorems:
heap-sep
/zheap/
sep
iter-n
/zheap/
Sep-rec
zbranch-array-ops
/
key-range-replace-branches
set-union
/node-store/
delete-shift
array
/address-set-array/
Extension
iter-n
/zheap/
Sep-unfold
Used simplifier rules:
set-basic
/node-store/
sub-one-02
set-union
/node-store/
One
set-basic
/node-store/
sub-in
set-basic
/node-store/
in-04
set-union
/node-store/
del-addeq-05
set-union
/node-store/
del-e-01
heap-sep
/zheap/
true-rev
heap-sep
/zheap/
true-and
heap-sep
/zheap/
emp-sep
set-union
/node-store/
del-e-02
set-basic
/node-store/
one-size
set-basic
/node-store/
size-one-01
zbranch-array-ops
/
unmodified-same-payload
set-basic
/node-store/
size-zero-01
zbranch-array-ops
/
unmodified-clean-leaf
set-basic
/node-store/
ne-01
nat-basic
/
succ
nat
/
elim-pred-c
constants
/
branchsize-0
existential
/zheap/
exists-shift
nat
/
ler
nat
/
lep-02
zbranch
/
elim-01
nat-basic
/
zero
nat
/
fle
oelem
/nat-set/
irreflexivity
nat
/
lep
zbranch
/
inj
zbranch-array-ops
/
unmodified-clean-fwd-zbrar
set-basic
/node-store/
sub-idem
zbranch
/
test-03
zbranch
/
sel-03
zbranch
/
sel-01
heap-sep
/zheap/
prop
heap-sep
/zheap/
and
heap-sep
/zheap/
sep-com
heap-sep
/zheap/
sep-ass
heap-sep
/zheap/
and-com
heap-sep
/zheap/
and-ass
heap-sep
/zheap/
prop-shift
nat
/
elim-sub
nat
/
succ-01
nat-basic
/
l-02
nat-basic
/
add-base
nat
/
add-01
nat-basic
/
l-01
nat-basic
/
eq-01
nat
/
eqle-one
nat
/
lels-03
nat
/
anti
nat
/
let
nat-basic
/
f
nat
/
le-ls-simp
nat
/
le-def
zbranch-array-ops
/
nsize-size
zbranch-array-ops
/
unmodified-clean-eq-keys
set-basic
/node-store/
in-03
store+set
/index-store-address-store/
Dom
nat
/
lez
address-set-array-ops
/
union-subset
set-basic
/node-store/
sub-add-03
nat-basic
/
oz
set-basic
/node-store/
Size-insert
set-basic
/node-store/
eq-01
set-basic
/node-store/
ne
set-union
/node-store/
del-addeq-04
nat-basic
/
lf-01
nat
/
fle-01
nat
/
lels
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04