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Theorem path-unfold
⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
abs-meta-h
,
abs-nlinks-h
,
abs-paths-eq
,
abs-unshared-h
,
path-fold
,
path-unfold-wand
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 28
Used lemmas:
entries-recdel
,
entries-dom1
,
entries-dom2
,
absc-entries
,
absc-dnode-rec
,
abs-dnode
,
absc-emp
,
Used spec theorems:
heap-sep
/dir-heap/
Eq-P
Used simplifier rules:
maplet
/dir-heap/
ex1-shift
directory-tree
/
split-in
list
/path/
c
directory-tree
/
one-inf
abstract-dir
/
elim
maplet
/dir-heap/
eq-objs
directory-tree
/
nil-in
directory-tree
/
nil-at
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
false-rev
heap-sep
/dir-heap/
falseH
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
maplet
/dir-heap/
ex3-shift
directory-tree
/
at-dnode
heap-sep
/dir-heap/
prop-shift
list
/path/
a
directory-tree
/
one-at
directory-tree
/
one-ind
abstract-dir
/
sel-09
abstract-dir
/
sel-03
abstract-dir
/
sel-04
heap-sep
/dir-heap/
true-rev
heap-sep
/dir-heap/
true-and
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com