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Theorem path-in-last

⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries)

Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by: refine-link, refine-mkdir, refine-readmeta, refine-rmdir, refine-unlink,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: path-in, path-in-eq,
Used spec theorems:
- Used simplifier rules: