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Proof step 63 from proof inv-link (previous step)

dirs[ino0] = mkdir(m, md, # links(ino0, dirs), m1, entries), dirs[ino0] = mkdir(m0, md0, m2, m3, entries0), err = ESUCCESS, inode = mkinode(ino0, md, true, # links(ino0, dirs), m1, m), afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino0 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_iget#(mkdentry(str, entries[str]).ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR; c_inode := inode; old_dent := mkdentry(str, entries0[str]); if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), err = ESUCCESS, inode = mkinode(ino0, md0, true, # links(ino0, dirs), m3, m0), p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, str ∈ entries0, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_iget#(mkdentry(str, entries0[str]).ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR; c_inode := inode; old_dent := mkdentry(str, entries0[str]); if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base