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Theorem dir-entry

⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries → (entries[str] ∈ dirs ↔ tree[p + str '].dir?)

Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by: dir-empty, fid-ino-entry, refine-create, refine-link, refine-mkdir, refine-rmdir, refine-unlink,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas: path-in-eq, path-in, make-abs-fold-work,
Used spec theorems:
- vfs-abs/abs-dir-h
- afs-base/path-trans
Used simplifier rules:
- afs-base/isexpath
- afs-base/afs-cons-dir-nlink
- afs-base/path-in-dirs
- list/path/a
- list/path/e-02
- list/path/Last
- heap-sep/dir-heap/sep-com
- heap-sep/dir-heap/sep-ass
- heap-sep/dir-heap/emp-sep
- afs-base/afs-cons-notfile
- afs-base/path-one
- abstract-dir/sel-09
- afs-base/afs-cons-in-next