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Proof step 31 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m4, dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, m4, content), ¬ boolvar, c_inode = mkinode(m1, md0, boolvar, m4, m5, m6), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[entries0[str], mkfile(m0, md1, m4 - 1, content)], m1 = entries0[str], m5 = 0, afs-cons(dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, 1 ≤ m4, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); 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), m4 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs0), content), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[entries0[str], mkfile(m0, md1, # links(entries0[str], dirs0) - 1, content)], # links(entries0[str], dirs0) ≠ 0, afs-cons(dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, 1 ≤ # links(entries0[str], dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m6); 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 := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)