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Proof step 61 from proof inv-link (previous step)

dirs[ino0] = mkdir(m, md, # links(ino0, dirs), m1, entries), dent = mkdentry(dent0.name, dirs[p_ino].entries[dent0.name]), dent0 = negdentry(str), err = ESUCCESS, err0 = ESUCCESS, inode = (ino0 ∈ dirs ⊃ mkinode(ino0, md, true, # links(ino0, dirs), m1, m) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ), p_ino = ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-lookup(p_ino, dent0, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), dent0.name ∈ dirs[p_ino].entries, ino0 ∈ dirs ⊦ ⟪afs_iget#(dent.ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR; c_inode := inode; old_dent := dent; 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 62:
dirs[ino0] = mkdir(m, md, # links(ino0, dirs), m1, entries), err = ESUCCESS, inode = mkinode(ino0, md, true, # links(ino0, dirs), m1, m), p ≠ ε, 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), ino0 ∈ dirs, str ∈ entries, 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, dirs[ino0].entries[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).entries = entries; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)% ⊦ negdentry(str).name = str; (s)