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Proof step 44 from proof inv-rename-dir-dentry (previous step)

old_child_inode.ino = old_dent.ino, new_child_inode.ino = new_dent.ino, dirs[m0] = mkdir(m6, md5, # links(m0, dirs), m9, entries0), dirs[m] = mkdir(m2, md3, # links(m, dirs), m5, entries2), dirs[entries2[str]] = mkdir(m1, md7, # links(entries2[str], dirs), m3, ∅), dirs[entries0[str0]] = mkdir(m4, md4, # links(entries0[str0], dirs), m7, entries), new_child_inode = mkinode(entries2[str], md, true, # links(entries2[str], dirs), m3, m1), new_dent = mkdentry(str, entries2[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m5, m2), old_child_inode = mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs), m7, m4), 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), dir-empty(new_dent.ino, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), valid-dentry(old_parent_inode.ino, old_dent, dirs, files), valid-dentry(new_parent_inode.ino, new_dent, dirs, files), valid-dir-inode(old_parent_inode, dirs, files), valid-dir-inode(new_parent_inode, dirs, files), valid-dir-inode(old_child_inode, dirs, files), valid-dir-inode(new_child_inode, dirs, files), str ∈ entries2, m0 ∈ dirs, m ∈ dirs, entries0[str0] ∈ dirs, entries2[str] ∈ dirs, str0 ∈ entries0, asynced → synced(files, icache, pcache), m = m0 → md1 = md2, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( 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)))), new_dent.ino = ROOT_INO, entries2[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, # links(entries0[str0], dirs) = dirs[entries0[str0]].nlink, # links(entries2[str], dirs) = dirs[entries2[str]].nlink, dirs[entries2[str]].entries = ∅, entries0[str0] = dirs[m0].entries[str0], entries2[str] = dirs[m].entries[str], dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries2), dirs[entries2[str]] = mkdir(dirs[entries2[str]].size, md7, dirs[entries2[str]].nlink, dirs[entries2[str]].nsubdirs, ∅), dirs[entries0[str0]] = mkdir(dirs[entries0[str0]].size, md4, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, entries), new_child_inode = mkinode(entries2[str], md, true, dirs[entries2[str]].nlink, dirs[entries2[str]].nsubdirs, dirs[entries2[str]].size), new_dent = mkdentry(str, entries2[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(entries0[str0], md0, true, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, dirs[entries0[str0]].size), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), entries2[str] ≠ ROOT_INO, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, str ∈ entries2, m0 ∈ dirs, m ∈ dirs, entries0[str0] ∈ dirs, entries2[str] ∈ dirs, str0 ∈ entries0, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, 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% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)