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Proof step 84 from proof inv-mkdir (previous step)

# links(ino0, dirs) = m0, dirs[ino0] = mkdir(m, md0, # links(ino0, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, ino ≠ 0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, ¬ ino ∈ dirs, ¬ ino ∈ files, ¬ str ∈ entries, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_mkdir_ino#(ino0, md, ino; dent, err, dirs); afs_inode_sync#(mkinode(ino0, md0, true, m0, m1, m); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 85:
# links(ino0, dirs) = m0, dirs[ino0] = mkdir(m, md0, # links(ino0, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, p_ino = ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [dirs[p_ino].entries[dent.name] := ino; dirs[p_ino].size := dirs[p_ino].size + 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs + 1; dirs := dirs ++ ino; dirs[ino] := mkdir(0, md, 1, 0, ∅); dent := mkdentry(dent.name, ino); err := ESUCCESS; afs_inode_sync#(mkinode(ino0, md0, true, m0, m1, m); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), ino = 0, ino ∈ dirs, ino ∈ files, str ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_mkdir_ino#(P_INO, MD, INO; DENT, ERR, DIRS) {DIRS[P_INO].entries[DENT.name] := INO; DIRS[P_INO].size := DIRS[P_INO].size + 1; DIRS[P_INO].nsubdirs := DIRS[P_INO].nsubdirs + 1; DIRS := DIRS ++ INO; DIRS[INO] := mkdir(0, MD, 1, 0, ∅); DENT := mkdentry(DENT.name, INO); ERR := ESUCCESS };