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Proof step 510 from proof refine-rename-dir-dentry (previous step)

(entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0) ;mkdir(m3, md4, # links(entries0[str0], cache_dirs), m11, ∅) ) .meta:= md = mkdir(m7, md5, m8, m9, entries1), (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0) ) = mkdir(m, md1, m2, m5, entries), cache_dirs[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], cache_dirs), m11, ∅), cache_dirs[m0] = mkdir(m1, md3, # links(m0, cache_dirs), m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, new_child_inode = new_child_inode0, new_child_inode0 = mkinode(entries0[str0], md, true, # links(entries0[str0], cache_dirs), m11, m3), new_dent = new_dent0, new_dent0 = mkdentry(str0, entries0[str0]), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m0, md0, true, # links(m0, cache_dirs), m4, m1), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m11, m3), old_dent = old_dent0, old_dent0 = mkdentry(str0, entries0[str0]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m0, md0, true, # links(m0, cache_dirs), m4, m1), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache[dentrykey(m0, str0), mkdentry(str0, entries0[str0])], cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))][entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7))], cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))][entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7))], cache_pcache), str0 ∈ entries0, entries0[str0] ∈ cache_dirs, m0 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7)) ], cache_pcache), links(m0, cache_dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = old_parent_inode ∧ (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = new_parent_inode ∧ mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), m11, m3) = old_child_inode ∧ (entries0[str0] ∈ cache_dirs0 ⊃ mkinode (entries0[str0], md, true, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nlink, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nsubdirs, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).size) ;mkinode(entries0[str0], cache_files[entries0[str0]].meta, false, cache_files[entries0[str0]].nlink, 0, cache_files[entries0[str0]].size) ) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries0[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0[m0, mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m0 ∧ entries0[str0] ∈ cache_dirs0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0) ;cache_dirs0[entries0[str0]] ) .meta:= md ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7)) ] ∧ (asynced ↔ asynced0)), ⟨let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); 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 := ?⟩ ( (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = old_parent_inode ∧ (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = new_parent_inode ∧ mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), m11, m3) = old_child_inode ∧ (entries0[str0] ∈ cache_dirs0 ⊃ mkinode (entries0[str0], md, true, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nlink, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nsubdirs, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).size) ;mkinode(entries0[str0], cache_files[entries0[str0]].meta, false, cache_files[entries0[str0]].nlink, 0, cache_files[entries0[str0]].size) ) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries0[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0[m0, mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m0 ∧ entries0[str0] ∈ cache_dirs0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0) ;cache_dirs0[entries0[str0]] ) .meta:= md ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7)) ] ∧ (asynced ↔ asynced0)), entries0[str0] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # 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)% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (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)% ⊦ 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).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (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)% ⊦ mkdentry(str, m).name = str; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)