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Proof step 247 from proof refine-unlink (previous step)

# entries0 = m0 + 1, files0[entries0[str]] = mkfile(m1, md1, # links(entries0[str], dirs0), content0), dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files = files0[ino, files0[ino].nlink:= (files0[ino].nlink - 1)], fs = abs-files(files0), ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), entries0[str] ∈ files0, ino1 ∈ dirs0, str ∈ entries0, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], files0[ino].nlink ≥ 1, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino1, md0, true, # links(ino1, dirs0), m3, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md1, false, # links(entries0[str], dirs0), 0, m1); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), entries0 = ∅, root[q + str '].dir?, entries0[str] ∈ dirs, entries0[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 248:
# entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, # links(entries0[str], dirs0), content0), files = files0[entries0[str], mkfile(m1, md1, # links(entries0[str], dirs0) - 1, content0)], # links(entries0[str], dirs0) ≠ 0, entries0 ≠ ∅, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ files0, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], 1 ≤ # links(entries0[str], dirs0), ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ entries0[str] ∈ dirs, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino1, md0, true, # links(ino1, dirs0), m3, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md1, false, # links(entries0[str], dirs0), 0, m1); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨fs := abs-files(files0); posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

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)