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Proof step 341 from proof refine-link (previous step)

fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs[ri[dentrykey(ino0, str)]] = dentrynode(key, fs[ri[dentrykey(ino2, str)]].ino), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), c_inode = p_inode1, dirs = abs-dirs(fs, ri), err = err1, files = abs-files(fs, ri), new_dent = old_dent0, old_dent = mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino), old_dent0 = negdentry(str0), p_inode = p_inode0, p_inode0 = mkinode(m, md, true, m0, m1, m2), p_inode1 = mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6), fs[ri[dentrykey(ino2, str)]].dentry?, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(ino0)]].directory, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[dentrykey(ino2, str)] ∈ fs, dentrykey(ino0, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino2, str) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(ino0) ∈ ri, ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)] ∈ fs, inodekey(fs[ri[dentrykey(ino2, str)]].ino) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, inodekey(ino2) ∈ ri, ⌊err0⌋ , asynced → boolvar0, m3 ≠ 0 ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, fs[ri[inodekey(ino2)]].nlink ≠ 0 ∨ ino2 = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs[ri[dentrykey(ino2, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2) = p_inode ∧ mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ err0 = err), ⟨let p_ino = p_inode.ino in {dirs[p_ino].entries[new_dent.name] := old_dent.ino; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2) = p_inode ∧ mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ err0 = err), fs[ri[dentrykey(ino2, str)]].ino = 0, m = 0, dentrykey(m, str0) ∈ ri, m3 = 0 ∧ fs[ri[dentrykey(ino2, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 342:
fs[ri[dentrykey(ino2, str)]].ino = fs[ri[dentrykey(ino, str)]].ino, fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino, str)]].ino, fs[ri[inodekey(fs[ri[dentrykey(ino, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs[ri[dentrykey(ino0, str)]] = dentrynode(key, fs[ri[dentrykey(ino, str)]].ino), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs[ri[dentrykey(ino, str)]].ino ≠ 0, m ≠ 0, fs[ri[dentrykey(ino2, str)]].dentry?, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(ino0)]].directory, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, ri[dentrykey(ino2, str)] ∈ fs, dentrykey(ino0, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino2, str) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(ino0) ∈ ri, ri[inodekey(fs[ri[dentrykey(ino, str)]].ino)] ∈ fs, inodekey(fs[ri[dentrykey(ino, str)]].ino) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, inodekey(ino2) ∈ ri, ⌊err0⌋ , ¬ dentrykey(m, str0) ∈ ri, asynced → boolvar0, links(ino, abs-dirs(fs, ri)) ≠ ∅ ∨ ino = ROOT_INO, m3 ≠ 0 ∨ fs[ri[dentrykey(ino, str)]].ino = ROOT_INO, fs[ri[inodekey(ino2)]].nlink ≠ 0 ∨ ino2 = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs[ri[dentrykey(ino, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino, str)]].ino = ROOT_INO ⊦ ⟨let p_ino = m in {dirs := abs-dirs(fs, ri) [p_ino, abs-dirs(fs, ri)[p_ino].entries:= abs-dirs(fs, ri)[p_ino].entries[str0, mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino] ]; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino in {files := abs-files(fs, ri); afs_inc_nlink#(ino; dirs, files)}; new_dent := mkdentry(str0, mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino); afs_inode_sync#(mkinode(m, md, true, m0, m1, m2); dirs, files); afs_inode_sync#(mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino).ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2) = p_inode ∧ mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ err0 = err), m3 = 0 ∧ fs[ri[dentrykey(ino, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%⊦ 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)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (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)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (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)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (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)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (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)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)