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Theorem btree-refed-subseteq-alladrs
⊦ ((btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P))(zh) → as ⊆ alladrs
Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by:
btree-adrs
,
btree-as-empty
,
btree-as-empty-rev
,
btree-clean-adr-in
,
btree-clean-alladrs
,
btree-clean-fwd
,
btree-clean-fwd-strong
,
btree-dirty-adr-notin
,
btree-inv-alloc
,
btree-inv-clean-commit
,
btree-inv-crash
,
btree-inv-format
,
btree-inv-remove-refsize0
,
btree-inv-root-neq-null-fwd
,
btree-inv-root-null
,
btree-inv-root-null-or-clean
,
btree-istore-reduce
,
btree-istore-reduce-refed
,
btree-istore-restrict
,
btree-istore-restrict-to-as
,
btree-leaf-adr
,
btree-leaf-fwd
,
btree-mark-dirty
,
btree-null
,
btree-remove-context
,
btree-repl-dirty-address
,
btree-reset-root-frame
,
btree-restrict-union-proper
,
btree-ri-unique
,
btree-root-in-heap
,
btree-write-node
,
btree-write-other
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 32
Used lemmas:
nat-le-eq
,
btree-imp-dirty
,
maplet-null
,
bnode
,
bleaf
,
btree
,
Used spec theorems:
set-union
/node-store/
delete-shift
set-basic
/node-store/
sub-insert-01
iter-n
/zheap/
Sep-unfold
Used simplifier rules:
heap-sep
/zheap/
emp-sep
set-union
/node-store/
del-e-02
set-basic
/node-store/
one-size
set-basic
/node-store/
in-06
set-basic
/node-store/
size-one-01
set-basic
/node-store/
in-04
set-basic
/node-store/
subset-empty
set-basic
/node-store/
sub-one-02
nat-basic
/
succ
set-basic
/node-store/
size-zero-01
set-basic
/node-store/
ne-01
existential
/zheap/
exists-shift
nat
/
elim-pred-c
constants
/
branchsize-0
nat-basic
/
f
nat
/
eqle-one
nat
/
succ-01
set-basic
/node-store/
Size-insert
set-basic
/node-store/
ne
zbranch-array-ops
/
unmodified-dirty
set-basic
/node-store/
sub-insert
set-union
/node-store/
del-in
heap-sep
/zheap/
prop
heap-sep
/zheap/
and
heap-sep
/zheap/
and-com
heap-sep
/zheap/
and-ass
heap-sep
/zheap/
prop-shift
nat
/
add-01
nat-basic
/
add-base
nat
/
le-ls-simp
nat
/
elim-sub
nat
/
lep
zbranch
/
elim-01
address-set-array-ops
/
subseteq-union-one
nat-basic
/
lf-01
nat
/
fle-01
nat-basic
/
s-04
nat
/
lez
address-set-array-ops
/
union-subset
set-basic
/node-store/
subset-insert-same
set-basic
/node-store/
in-03
zbranch
/
inj
zbranch-array-ops
/
unmodified-clean-fwd-zbrar
zbranch-array-ops
/
nsize-size
nat
/
le-def
zbranch
/
test-03
heap-sep
/zheap/
sep-ass
heap-sep
/zheap/
sep-com
set-basic
/node-store/
sub-ntrans
nat
/
ler
nat
/
lels
nat-basic
/
a
nat-basic
/
c
nat-basic
/
oz
address-set-array-ops
/
subseteq-union-one-add