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Proof step 20 from proof inv-unlink (previous step)

# links(entries[str], dirs0) = c_inode.nlink, # links(m, dirs0) = m2, c_inode.ino = entries[str], c_inode.nsubdirs = 0, dirs0[m] = mkdir(m1, md0, m2, m3, entries), entries[str] = entries0[str], files[entries[str]] = mkfile(m0, md1, c_inode.nlink, content), dirs0[m] = mkdir(m1, md2, m2, m3, entries0), dirs = dirs0[m, (dirs0[m].entries:= (entries0 -- str)).size:= (m1 - 1)], afs-cons(dirs0, files), entries[str] ∈ files, str ∈ entries, m ∈ dirs0, str ∈ entries0, 1 ≤ m1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, m2, m3, m1); dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), m1 = 0, c_inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# links(entries0[str], dirs0) = c_inode.nlink, c_inode.ino = entries0[str], c_inode.nsubdirs = 0, files[entries0[str]] = mkfile(m0, md1, c_inode.nlink, content), dirs0[m] = mkdir(m1, md2, # links(m, dirs0), m3, entries0), dirs = dirs0[m, mkdir(m1 - 1, md2, # links(m, dirs0), m3, entries0 -- str)], m1 ≠ 0, afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files, 1 ≤ m1, ¬ c_inode.directory, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m1); dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base