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Theorem absc-drop
⊦ p ≠ ε ∧ q ⊑ p ∧ parent(p) ∈ tree ∧ tree[parent(p)].dir? → abs|(tree[p, tree0], ino0, q, ino1) = abs|(tree, ino0, q, ino1)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 27
Used lemmas:
absc-entries
,
absc-dnode-rec
,
absc-emp
,
Used spec theorems:
heap-sep
/dir-heap/
Eq-P
list-last
/path/
bapp
Used simplifier rules:
heap-sep
/dir-heap/
true-rev
heap-sep
/dir-heap/
true-and
directory-tree
/
put-here
list-last
/path/
prefix-empty
directory-tree
/
nil-in
directory-tree
/
isdnode
heap-sep
/dir-heap/
emp-sep
directory-tree
/
at-dnode
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
maplet
/dir-heap/
ex3-shift
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
prop-shift
store
/directory-tree-inst/
Del-rec-same
directory-tree-base
/
At-same
directory-tree
/
put-rec
directory-tree
/
in-dnode
abstract-dir
/
elim
maplet
/dir-heap/
eq-objs
abstract-dir
/
sel-09
abstract-dir
/
sel-04
abstract-dir
/
sel-03
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
list-last
/path/
b-01
directory-tree
/
fnode-notin
list
/path/
c
list
/path/
c-03
list
/path/
a
list
/path/
e-01
list-last
/path/
prefix-rec-03
list
/path/
app
list-last
/path/
butlast-one
directory-tree
/
nil-at
directory-tree
/
isfnode
list-data
/path/
elim-list-c