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Proof step 169 from proof inv-unlink (previous step)

files0[entries[str]] = mkfile(m0, md, # links(entries[str], dirs0), content), dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), dirs = dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2, entries -- str)], files = files0[ino, files0[ino].nlink:= (files0[ino].nlink - 1)], ino = mkdentry(str, entries[str]).ino, mkdentry(str, entries[str]).dentry?, dom of < ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, entries[str] ∈ files0, str ∈ entries, 1 ≤ m, files0[ino].nlink ≥ 1, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino1, md1, true, # links(ino1, dirs0), m2, m); dirs, files); afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m0); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), m = 0, entries[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 170:
dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), files0[entries[str]] = mkfile(m0, md, # links(entries[str], dirs0), content), dirs = dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2, entries -- str)], files = files0[entries[str], mkfile(m0, md, # links(entries[str], dirs0) - 1, content)], # links(entries[str], dirs0) ≠ 0, m ≠ 0, dom of < ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries, entries[str] ∈ files0, ino1 ∈ dirs0, 1 ≤ # links(entries[str], dirs0), 1 ≤ m, ¬ entries[str] ∈ dirs0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino1, md1, true, # links(ino1, dirs0), m2, m); dirs, files); afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m0); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ 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]% ⊦ mkfile(m, md, m0, content).nlink:= m2 = mkfile(m, md, m2, content); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkdentry(str, m).ino = m; (s)