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Proof step 22 from proof inv-rename-file-dentry (previous step)

dirs[m] = mkdir(m5, md5, # links(m, dirs), m7, entries), files[entries[str]] = mkfile(m1, md3, # links(entries[str], dirs), content), files[entries0[str0]] = mkfile(m4, md4, # links(entries0[str0], dirs), content0), dirs[m0] = mkdir(m6, md6, m8, m9, entries0), new_child_inode = mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m7, m5), old_child_inode = mkinode(entries0[str0], md0, false, # links(entries0[str0], dirs), 0, m3), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md2, true, m8, m9, m6), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries0[str0] ∈ files, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
dirs[m] = mkdir(m5, md5, # links(m, dirs), m7, entries), files[entries[str]] = mkfile(m1, md3, # links(entries[str], dirs), content), files[entries0[str0]] = mkfile(m4, md4, # links(entries0[str0], dirs), content0), dirs[m0] = mkdir(m6, md6, # links(m0, dirs), m9, entries0), new_child_inode = mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m7, m5), old_child_inode = mkinode(entries0[str0], md0, false, # links(entries0[str0], dirs), 0, m3), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md2, true, # links(m0, dirs), m9, m6), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries0[str0] ∈ files, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base