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Proof step 23 from proof refine-rename-file-dentry (previous step)

# links(m3, cache_dirs) = m1, # links(m, cache_dirs) = m16, cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = mkinode(entries[str], md1, false, m14, 0, m10), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m17, m11), old_child_inode = mkinode(entries0[str0], md2, false, m15, 0, m13), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m2, m0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries, str0 ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, entries[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md, true, m16, m17, m11); old_parent_inode0 := mkinode(m3, md0, true, m1, m2, m0); new_child_inode0 := mkinode(entries[str], md1, false, m14, 0, m10); old_child_inode0 := mkinode(entries0[str0], md2, false, m15, 0, m13); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: cache-asm name: inv-rename-file-dentry seq: 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), 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-file-inode(old_child_inode, 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, old_child_inode.ino = old_dent.ino, new_child_inode.ino = new_dent.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))) subst: [asynced0, dcache, icache, files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, pcache, asynced] → [cache_asynced, cache_dcache, cache_icache, cache_files, cache_dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, cache_pcache, cache_sync] flags: List([[1,0,0]])

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