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Proof step 9 from proof refine-readdir (previous step)

err = err0, ino = ROOT_INO, root.dir?, dom of < ino0, 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_walk#(path, user, dirs, files, asynced; ino, err); strings := strings0; if err = ESUCCESS then {mode := MODE_R; isdir := true; choose inode with true in {vfs_may_open#(ino, isdir, mode, user, dirs, files, asynced; inode, err); if err = ESUCCESS then afs_readdir#(inode, 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

Rule argument

spec: vfs-asm name: walk-prepost seq: ino = ROOT_INO, afs-cons(dirs, files) ⊦ ⟪vfs_walk#(p, user, dirs, files, asynced; ino, err)⟫ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, ROOT_INO, ino, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files))) subst: [asynced, files, dirs, user, p, err, ino] → [asynced, files, dirs, user, path, err, ino] flags: <all paths>

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