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Proof step 42 from proof inv-rename-file-dentry (previous step)

dirs[m] = mkdir(m4, md4, # links(m, dirs), m7, entries1), files[entries1[str]] = mkfile(m5, md7, # links(entries1[str], dirs), content1), files[entries[str0]] = mkfile(m1, md3, # links(entries[str0], dirs), content), dirs[m0] = mkdir(m6, md5, # links(m0, dirs), m9, entries), new_child_inode = mkinode(entries1[str], md, false, # links(entries1[str], dirs), 0, m2), new_dent = mkdentry(str, entries1[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m7, m4), old_child_inode = mkinode(entries[str0], md0, false, # links(entries[str0], dirs), 0, m3), old_dent = mkdentry(str0, entries[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), str0 ∈ entries, m ∈ dirs, m0 ∈ dirs, entries1[str] ∈ files, entries[str0] ∈ files, str ∈ entries1, ¬ entries1[str] ∈ dirs, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1); 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)))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: afs-cons-rename-file-dentry seq: afs-cons(dirs, files), valid-dentry(old_parent_inode.ino, old_dent, dirs, files), valid-dir-inode(old_parent_inode, dirs, files), valid-dir-inode(new_parent_inode, dirs, files), valid-file-inode(old_child_inode, dirs, files), old_child_inode.ino = old_dent.ino, valid-dentry(new_parent_inode.ino, new_dent, dirs, files), valid-file-inode(new_child_inode, dirs, files), new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, new_child_inode.ino = new_dent.ino ⊦ ⟪afs_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files ; asynced)⟫ afs-cons(dirs, files) subst: [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced] → [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced1] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (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)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)