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Proof step 9 from proof refine-renam (previous step)

p_inode1.ino = cache_dirs[m].entries[str], afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, new_child_inode = p_inode2, new_dent = old_dent1, new_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), old_child_inode = p_inode1, old_dent = mkdentry(str, p_inode1.ino), old_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].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, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, m3 = m → md0 = md, cache_sync → synced(cache_files, cache_icache, cache_pcache), p_inode1.ino ∈ cache_dirs ∧ p_inode1.nlink = cache_dirs[p_inode1.ino].nlink ∧ p_inode1.size = cache_dirs[p_inode1.ino].size ∧ p_inode1.nsubdirs = cache_dirs[p_inode1.ino].nsubdirs ∧ p_inode1.directory ∨ p_inode1.ino ∈ cache_files ∧ p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode1.ino].nlink ∧ p_inode1.nsubdirs = 0 ∧ ¬ p_inode1.directory, p_inode1.ino ∈ cache_dirs ∨ p_inode1.ino ∈ cache_files, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.negdentry? ∨ (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (old_dent1.ino ∈ cache_dirs ∨ old_dent1.ino ∈ cache_files) ∧ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.ino = cache_dirs[m3].entries[old_dent1.name] ∧ old_dent1.dentry? ∧ ( p_inode2.ino ∈ cache_dirs ∧ p_inode2.nlink = cache_dirs[p_inode2.ino].nlink ∧ p_inode2.size = cache_dirs[p_inode2.ino].size ∧ p_inode2.nsubdirs = cache_dirs[p_inode2.ino].nsubdirs ∧ p_inode2.directory ∨ p_inode2.ino ∈ cache_files ∧ p_inode2.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode2.ino].nlink ∧ p_inode2.nsubdirs = 0 ∧ ¬ p_inode2.directory) ∧ p_inode2.ino = old_dent1.ino ∧ (old_dent1.ino ∈ cache_files ↔ p_inode1.ino ∈ cache_files) ∧ (old_dent1.ino ∈ cache_dirs → old_dent1.ino ≠ ROOT_INO ∧ cache_dirs[old_dent1.ino].entries = ∅) ⊦ ⟪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)⟫ ⟨old_dent0 := mkdentry(str, p_inode1.ino); p_inode := mkinode(m, md, true, m0, m1, m2); p_inode0 := mkinode(m3, md0, true, m4, m5, m6); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
p_inode1.ino = cache_dirs[m].entries[str], afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m2 = cache_dirs[m].size, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, new_child_inode = p_inode2, new_dent = old_dent1, new_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), old_child_inode = p_inode1, old_dent = mkdentry(str, p_inode1.ino), old_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), p_inode2 = mkinode(m7, md1, boolvar, m8, m9, m10), 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), m ∈ cache_dirs, str ∈ cache_dirs[m].entries, m3 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m → md0 = md, (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.negdentry? ∨ (links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (old_dent1.ino ∈ cache_dirs ∨ old_dent1.ino ∈ cache_files) ∧ old_dent1.name ∈ cache_dirs[m3].entries ∧ old_dent1.ino = cache_dirs[m3].entries[old_dent1.name] ∧ old_dent1.dentry? ∧ ( m7 ∈ cache_dirs ∧ m8 = cache_dirs[m7].nlink ∧ m10 = cache_dirs[m7].size ∧ m9 = cache_dirs[m7].nsubdirs ∧ boolvar ∨ m7 ∈ cache_files ∧ m8 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m7].nlink ∧ m9 = 0 ∧ ¬ boolvar) ∧ m7 = old_dent1.ino ∧ (old_dent1.ino ∈ cache_files ↔ p_inode1.ino ∈ cache_files) ∧ (old_dent1.ino ∈ cache_dirs → old_dent1.ino ≠ ROOT_INO ∧ cache_dirs[old_dent1.ino].entries = ∅), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, p_inode1.ino ∈ cache_dirs ∨ p_inode1.ino ∈ cache_files, p_inode1.ino ∈ cache_dirs ∧ p_inode1.nlink = cache_dirs[p_inode1.ino].nlink ∧ p_inode1.size = cache_dirs[p_inode1.ino].size ∧ p_inode1.nsubdirs = cache_dirs[p_inode1.ino].nsubdirs ∧ p_inode1.directory ∨ p_inode1.ino ∈ cache_files ∧ p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode1.ino].nlink ∧ p_inode1.nsubdirs = 0 ∧ ¬ p_inode1.directory ⊦ ⟪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)⟫ ⟨old_dent0 := mkdentry(str, p_inode1.ino); p_inode := mkinode(m, md, true, m0, m1, m2); p_inode0 := mkinode(m3, md0, true, m4, m5, m6); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)

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] → [p_inode2, m7, md1, boolvar, m8, m9, m10]

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: p_inode2, m7, md1, boolvar, m8, m9, m10