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Theorem entries-any
sdt ≠ ∅ ⊦ ((abs(sdt, sdi) * D))(dirs) ↔ (∃ tree, ino, str, sdi0, sdt0. ¬ str ∈ sdt0 ∧ sdt = sdt0[str, tree] ∧ ¬ str ∈ sdi0 ∧ sdi = sdi0[str, ino] ∧ ((abs(tree, ino) * abs(sdt0, sdi0) * D))(dirs))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
abs-has-rootpath-h
,
entries-dom
,
entries-empty
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas:
abs-rec
,
Used spec theorems:
store
/directory-tree-inst/
exnotempty
Used simplifier rules:
heap-sep
/dir-heap/
true-and
store
/dir-entries/
notin-del-notin
store
/dir-entries/
Del-rec-same
store
/dir-entries/
At-same
heap-sep
/dir-heap/
true-rev
store
/dir-entries/
insin
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
prop-shift
store
/dir-entries/
Del-in
store
/dir-entries/
del-put
store
/dir-entries/
ins-same-01
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com