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Theorem subdirs-add-entry

⊦ ino ∈ dirs → subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries[str, ino0])]) = (ino0 ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) ++ str ;(str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) -- str ;subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) ) )

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: subdirs-put,
Used by units in proved state: afs-asm,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 12
Used lemmas: subdirs,
Used spec theorems:
- set-basic/dir-entries/Extension
Used simplifier rules:
- set-basic/dir-entries/In-insert
- store/dir-entries/insin
- store/dir-entries/At-same
- store/dir-entries/At-other
- store/dir-entries/in-neq
- set-union/dir-entries/Delete
- abstract-dir/sel-09
- heap/dir-heap/at-write
- heap/dir-heap/in-write