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Proof step 13 from proof refine-rename-dir-dentry (previous step)

cache_dirs[cache_dirs[m].entries[str]].entries = ∅, old_child_inode0.ino = cache_dirs[m3].entries[str0], old_child_inode0.nlink = cache_dirs[old_child_inode0.ino].nlink, old_child_inode0.nsubdirs = cache_dirs[old_child_inode0.ino].nsubdirs, old_child_inode0.size = cache_dirs[old_child_inode0.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m10 = cache_dirs[cache_dirs[m].entries[str]].size, m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m7 = cache_dirs[m].entries[str], m8 = cache_dirs[cache_dirs[m].entries[str]].nlink, m9 = cache_dirs[cache_dirs[m].entries[str]].nsubdirs, new_child_inode = mkinode (cache_dirs[m].entries[str], md1, true, cache_dirs[cache_dirs[m].entries[str]].nlink, cache_dirs[cache_dirs[m].entries[str]].nsubdirs, cache_dirs[cache_dirs[m].entries[str]].size), new_dent = mkdentry(str, cache_dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), old_child_inode = old_child_inode0, old_dent = mkdentry(str0, old_child_inode0.ino), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), cache_dirs[m].entries[str] ≠ ROOT_INO, old_child_inode0.directory, 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 ∈ cache_dirs[m].entries, str0 ∈ cache_dirs[m3].entries, cache_dirs[m].entries[str] ∈ cache_dirs, old_child_inode0.ino ∈ cache_dirs, m ∈ cache_dirs, m3 ∈ cache_dirs, 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, m7); old_dent0 := mkdentry(str0, old_child_inode0.ino); new_parent_inode0 := mkinode(m, md, true, m0, m1, m2); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); new_child_inode0 := mkinode(m7, md1, true, m8, m9, m10); 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
cache_dirs[cache_dirs[m].entries[str]].entries = ∅, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, boolvar, err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m10 = cache_dirs[cache_dirs[m].entries[str]].size, m11 = cache_dirs[m3].entries[str0], m12 = cache_dirs[m11].nlink, m13 = cache_dirs[m11].nsubdirs, m14 = cache_dirs[m11].size, m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m7 = cache_dirs[m].entries[str], m8 = cache_dirs[cache_dirs[m].entries[str]].nlink, m9 = cache_dirs[cache_dirs[m].entries[str]].nsubdirs, new_child_inode = mkinode (cache_dirs[m].entries[str], md1, true, cache_dirs[cache_dirs[m].entries[str]].nlink, cache_dirs[cache_dirs[m].entries[str]].nsubdirs, cache_dirs[cache_dirs[m].entries[str]].size), new_dent = mkdentry(str, cache_dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(m11, md2, boolvar, m12, m13, m14), old_dent = mkdentry(str0, m11), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), 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), m3 ∈ cache_dirs, m ∈ cache_dirs, m11 ∈ cache_dirs, cache_dirs[m].entries[str] ∈ cache_dirs, str0 ∈ cache_dirs[m3].entries, str ∈ cache_dirs[m].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = 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, m7); old_dent0 := mkdentry(str0, m11); new_parent_inode0 := mkinode(m, md, true, m0, m1, m2); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); new_child_inode0 := mkinode(m7, md1, true, m8, m9, m10); 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)), cache_dirs[m].entries[str] = ROOT_INO

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [old_child_inode0, m11, md2, boolvar, m12, m13, m14]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: old_child_inode0, m11, md2, boolvar, m12, m13, m14