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Proof step 19 from proof refine-rename-file-negdentry (previous step)

# links(m3, cache_dirs) = m1, # links(m, cache_dirs) = m12, cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m13, m8), old_child_inode = mkinode(entries0[str], md1, false, m11, 0, m10), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m2, m0), 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), m ∈ cache_dirs, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, ¬ str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, 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)⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m12, m13, m8); old_parent_inode0 := mkinode(m3, md0, true, m1, m2, m0); old_child_inode0 := mkinode(entries0[str], md1, false, m11, 0, 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))

User applied rule call right

And obtained the following new goals

Proof step 20:
# links(m, cache_dirs) = m12, # links(m3, cache_dirs) = m1, asynced1 ↔ cache_asynced, cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dcache = cache_dcache, dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m13, m8), old_child_inode = mkinode(entries0[str], md1, false, m11, 0, m10), old_dent = mkdentry(str, entries0[str]), 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 ∈ entries0, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) then let asynced0 = new_dent.dentry? in {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 asynced0 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)}} else abort⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m12, m13, m8); old_parent_inode0 := mkinode(m3, md0, true, m1, m2, m0); old_child_inode0 := mkinode(entries0[str], md1, false, m11, 0, 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 = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ icache ∧ (afs_asynced ↔ asynced1)), str0 ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_rename# (; OLD_PARENT_INODE, NEW_PARENT_INODE, OLD_CHILD_INODE, NEW_CHILD_INODE, OLD_DENT, NEW_DENT, ERR, DIRS, FILES, ICACHE, DCACHE, ASYNCED ) {if pre-rename (OLD_PARENT_INODE, OLD_DENT, OLD_CHILD_INODE, NEW_PARENT_INODE, NEW_DENT, NEW_CHILD_INODE, DIRS, FILES) then let DENTP = NEW_DENT.dentry? in {afs_rename# (; OLD_PARENT_INODE, NEW_PARENT_INODE, OLD_CHILD_INODE, NEW_CHILD_INODE, OLD_DENT, NEW_DENT, ERR, DIRS, FILES ; ASYNCED); if ERR = ESUCCESS then let DIRTY = false in {icache_set#(OLD_PARENT_INODE, DIRTY; ERR, ICACHE); icache_set#(NEW_PARENT_INODE, DIRTY; ERR, ICACHE); if DENTP then icache_set# (NEW_CHILD_INODE, DIRTY; 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)}} else abort };