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Proof step 12 from proof refine-fsync (previous step)

asynced0 ↔ asynced, dirs0 = dirs, err = ESUCCESS, files0 = files, ino = ROOT_INO, p0 = path, user0 = user, 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)] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p0, ROOT_INO, ino, dirs0, files0) ∧ px-parent(user0, p0, ROOT_INO, dirs0, files0) ∨ err = ENOENT ∧ ¬ ispath(p0, ROOT_INO, dirs0, files0) ∨ err = EACCESS ∧ p0 ≠ ε ∧ (∃ p'. p' ⊑ parent(p0) ∧ ispath(p', ROOT_INO, dirs0, files0) ∧ ¬ px(user0, p', ROOT_INO, dirs0, files0)) → [if err = ESUCCESS then let isdir = false in vfs_may_open#(ino, isdir, MODE_R, user, dirs, files, asynced; inode, err); if err = ESUCCESS then afs_fsync#(inode, isdir, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
err = ESUCCESS, 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)] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(path, ROOT_INO, ino, dirs, files) ∧ px-parent(user, path, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(path, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ path ≠ ε ∧ (∃ p'. p' ⊑ parent(path) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)) → [if err = ESUCCESS then let isdir = false in vfs_may_open#(ino, isdir, MODE_R, user, dirs, files, asynced; inode, err); if err = ESUCCESS then afs_fsync#(inode, isdir, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0))

Proof step 12 from proof refine-fsync (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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