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Theorem abs-fold-del-p
⊦ str ∈ entries ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt) ∧ ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries - 1, md, m0, m1, entries -- str) * abs(sdt -- str, entries -- str) * D))(dirs) → ((abs(tree -- (p + str '), ROOT_INO) * D))(dirs)
Type: A user defined theorem
Validity: The proof is valid.
Features: lss,
Comment:
Used by:
abs-fold-del
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 16
Used lemmas:
Used spec theorems:
directory-tree
/
split-del
vfs-abs
/
path-unfold
vfs-abs
/
abs-dnode
vfs-abs
/
absc-drop
Used simplifier rules:
store
/dir-entries/
Size-empty
store
/dir-entries/
Del-empty
vfs-abs
/
entries-empty
store
/dir-entries/
In-empty
nat
/
elim-pred-c
store
/dir-entries/
empty
directory-tree
/
del-here
maplet
/dir-heap/
ex1-shift
directory-tree
/
same-at
directory-tree
/
same-in
maplet
/dir-heap/
ex3-shift
nat-basic
/
c
nat-basic
/
a
nat-basic
/
add-base
nat
/
add-01
nat
/
pred-03
store
/dir-entries/
size
abstract-dir
/
sel-09
abstract-dir
/
sel-03
abstract-dir
/
sel-04
list-last
/path/
prefix-self
list
/path/
e-02
list
/path/
a
directory-tree
/
split-in
directory-tree
/
notdir-notin
list
/path/
e
directory-tree
/
nil-at
directory-tree
/
nil-in
vfs-abs
/
absc-emp
heap-sep
/dir-heap/
prop-shift
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
prop
directory-tree
/
nil-put
heap-sep
/dir-heap/
true-rev
heap-sep
/dir-heap/
true-and
path
/
parent-elim