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Proof step 465 from proof refine-rename-file-dentry (previous step)

# links(m3, cache_dirs) = m1, # links(m, cache_dirs) = m16, # links(entries1[str0], cache_dirs) = m7, # links(entries0[str], cache_dirs) = m5, asynced0 ↔ old_ino = new_ino ∧ new_dent = old_dent, asynced1 ↔ new_dent.dentry?, cache_files[entries0[str]] = mkfile(m0, md6, # links(entries0[str], cache_dirs), content3), cache_dirs[m3] = mkdir(m6, md9, # links(m3, cache_dirs), m15, entries1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m12, md3, # links(entries0[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), cache_dirs[m] = mkdir(m4, md8, # links(m, cache_dirs), m14, entries0), cache_files[entries1[str0]] = mkfile(m2, md7, # links(entries1[str0], cache_dirs), content1), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, asynced0, asynced1, dirs = dirs1[new_ino, dirs1[new_ino].entries:= dirs1[new_ino].entries[new_dent.name, old_dent.ino]], dirs0 = cache_dirs, dirs1 = dirs0[old_ino, dirs0[old_ino].entries:= (dirs0[old_ino].entries -- old_dent.name)], err = err0, files = cache_files, new_child_inode = mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10), new_dent = mkdentry(str, entries0[str]), new_ino = new_parent_inode.ino, new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m14, m4), old_child_inode = mkinode(entries1[str0], md2, false, # links(entries1[str0], cache_dirs), 0, m13), old_dent = mkdentry(str0, entries1[str0]), old_ino = old_parent_inode.ino, old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m15, m6), old_dent.dentry?, 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), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs0, files), synced(cache_dirs, cache_icache, cache_pcache), entries1[str0] ∈ cache_files, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries1, str ∈ entries0, 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 ⊦ [afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS; asynced := ?; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent1 := negdentry(old_dent.name); if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent1.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, dirs, files) ∧ dcache-cons(cache_dcache, dirs, files) ∧ pcache-cons(cache_pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries1[str0]); new_parent_inode0 := mkinode(m, md, true, m16, m14, m4); old_parent_inode0 := mkinode(m3, md0, true, m1, m15, m6); new_child_inode0 := mkinode(entries0[str], md1, false, m5, 0, m10); old_child_inode0 := mkinode(entries1[str0], md2, false, m7, 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_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))), entries0[str] ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 466:
# links(entries1[str0], cache_dirs) = cache_files[entries1[str0]].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, cache_files[entries1[str0]].nlink, content0), cache_dirs[m] = mkdir(cache_dirs[m].size, md9, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries1), cache_files[entries1[str0]] = mkfile(m0, md6, cache_files[entries1[str0]].nlink, content3), entries0[str0] = entries1[str0], entries1[str0] = cache_dirs[m].entries[str0], cache_files[entries1[str0]] = mkfile(m2, md7, cache_files[entries1[str0]].nlink, content1), cache_dirs[m] = mkdir(cache_dirs[m].size, md8, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, cache_dirs[m].entries:= (cache_dirs[m].entries -- str0).entries:= cache_dirs[m].entries], 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), str0 ∈ entries0, str0 ∈ entries1, m ∈ cache_dirs, entries1[str0] ∈ cache_files, str0 ∈ cache_dirs[m].entries, ¬ entries1[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size); dirs, cache_files); afs_inode_sync#(mkinode(m, md0, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size); dirs, cache_files); new_child_inode := mkinode(entries0[str0], md1, false, # links(entries0[str0], cache_dirs), 0, m10); afs_inode_sync#(new_child_inode; dirs, cache_files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, cache_files[new_child_inode.ino].meta, false, cache_files[new_child_inode.ino].nlink, 0, cache_files[new_child_inode.ino].size) ); old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ); err := ESUCCESS; asynced := ?; new_dent := mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries1[str0]).ino); old_dent1 := negdentry(mkdentry(str0, entries1[str0]).name); str := str0; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent1.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, dirs, cache_files) ∧ dcache-cons(cache_dcache, dirs, cache_files) ∧ pcache-cons(cache_pcache, dirs, cache_files) ∧ afs-cons(dirs, cache_files) ∧ synced(dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries1[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size); new_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries1[str0], md2, false, # links(entries1[str0], cache_dirs), 0, m13); cache_dirs0 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode(entries1[str0], md2, false, # links(entries1[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ entries[str] = ino ∧ str ∈ entries → entries[str, ino] = entries; (s)% ⊦ (entries -- str)[str, ino] = entries[str, ino]; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (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-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (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-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (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)% ⊦ ¬ mkdentry(str, m).negdentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, 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) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)% ⊦ mkdentry(str, m) = mkdentry(str0, m0) ↔ str = str0 ∧ m = m0; (ws)% ⊦ (ad.entries:= entries).entries = entries; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)