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Theorem path-split-wand
⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs(tree[p], ino1) * (abs(tree[p], ino1) -* abs(tree, ino0)))
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: 24
Proof steps: 47
Used lemmas:
entries-del
,
abs-rec
,
entries-dom1
,
entries-dom2
,
abs-dnode
,
Used spec theorems:
store
/directory-tree-inst/
exin
store
/dir-entries/
exin
heap-sep
/dir-heap/
sep-split-interactive
heap-sep
/dir-heap/
sep
heap-sep
/dir-heap/
wand
heap
/dir-heap/
disj-distr-uni
heap-sep
/dir-heap/
sep-ass
heap
/dir-heap/
uni-ass
heap-sep
/dir-heap/
split-union
heap-sep
/dir-heap/
sep-mp
Used simplifier rules:
maplet
/dir-heap/
ex1
directory-tree
/
nil-at
directory-tree
/
nil-in
heap-sep
/dir-heap/
wand-same-emp-p
directory-tree
/
split-in
list
/path/
c
directory-tree
/
one-inf
list
/path/
a
directory-tree
/
at-dnode
directory-tree
/
one-at
directory-tree
/
one-ind
abstract-dir
/
elim
heap-sep
/dir-heap/
trueH
heap-sep
/dir-heap/
true-rev
heap-sep
/dir-heap/
prop-shift
directory-tree-base
/
At-same
store
/dir-entries/
notin-del-notin
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
maplet
/dir-heap/
ex3
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01
store
/dir-entries/
Size-insert
abstract-dir
/
sel-03
abstract-dir
/
sel-04
store
/dir-entries/
Del-rec-same
store
/dir-entries/
At-same
store
/dir-entries/
insin
abstract-dir
/
sel-09
heap
/dir-heap/
disj-distr-uni-com
heap
/dir-heap/
disj-com-rw
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com