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Proof step 3 from proof refine-readdir (previous step)

err = err0, strings = strings0, root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ ⟪vfs_readdir#(path, user, dirs, files, asynced; strings, err)⟫ ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 4:
of-cons(of, dirs, files), afs-cons(dirs, files) ⊦ ⟪vfs_readdir#(p, user, dirs, files, asynced; strings, err)⟫ true
Proof step 5:
asynced0 ↔ asynced, dirs0 = dirs, err = err0, files0 = files, of0 = of, p0 = path, strings = strings0, user0 = user, root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [vfs_readdir#(path, user, dirs, files, asynced; strings, err)] ( true → ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err = err0))

Rule argument

spec: vfs-asm name: inv-readdir seq: of-cons(of, dirs, files), afs-cons(dirs, files) ⊦ ⟪vfs_readdir#(p, user, dirs, files, asynced; strings, err)⟫ true subst: [asynced, files, dirs, user, p, err, strings, of] → [asynced, files, dirs, user, path, err, strings, of] flags: <all paths>

Proof step 3 from proof refine-readdir (previous step)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

Additional information