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Theorem fids-put1
p ≠ ε ⊦ p ∈ tree0 ∧ tree0[parent(p)].dir? → tree0[p, tree1].fids = (tree0.fids \ tree0[p].fids) ∪ tree1.fids
Type: A user defined theorem
Validity: The proof is valid.
Features: s,
Comment:
Used by:
Used by units in proved state:
posix-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 24
Used lemmas:
fids-fnode
,
fids-ins
,
fids-dnode
,
fids-sub
,
Used spec theorems:
store
/directory-tree-inst/
exin
list-last
/path/
bapp
directory-tree
/
put-rec
bag-union
/fidbag/
union-diff-distr
bag-union
/fidbag/
count-subset
bag-union
/fidbag/
union
Used simplifier rules:
directory-tree
/
split-in
list
/path/
e-01
list
/path/
c
directory-tree
/
one-inf
directory-tree
/
one-at
directory-tree
/
at-dnode
directory-tree
/
one-ind
list
/path/
app
directory-tree
/
put-here
directory-tree
/
nil-at
bag-union
/fidbag/
union-diff-cancel
bag-union
/fidbag/
union-inj
list
/path/
a
directory-tree
/
at-dnode-same
store
/directory-tree-inst/
insin
directory-tree-base
/
In-insert
store
/directory-tree-inst/
insins
directory-tree-base
/
At-same
nat-basic
/
f
nat
/
le-def
nat
/
fle
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
bag-union
/fidbag/
union-diff-distr
bag-union
/fidbag/
union-ass
bag-union
/fidbag/
union-com