[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 300 from proof refine-unlink (previous step)

m5 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, 0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], fs1 = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], fs2 = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], key = inodekey(fs0[ri0[dentrykey(m, str)]].ino), key0 = dentrykey(m, mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', log2 = ((log0 + adr1 ') + adr2 ') + adr3 ', m3 = fs0[ri0[dentrykey(m, str)]].ino, m4 = m5 + 1, old_dent = mkdentry(str, m3), ri = ri2[key, adr], ri1 = ri0[inodekey(m), adr1], ri2 = ri1 -- key0, ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), ro1 = orphans(fs0, ri0), fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(m)]].directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).inode?, fs0[ri0[inodekey(m)]].inode?, inodenode(inodekey(m3), md0, false, m5, 0, m6).inode?, fo.inodes?, orphans(fs0, ri0).inodes?, ro0.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons(fs1, ri), key-cons(key, fs[adr]), log-cons(log0, fs0), log-cons(log1, fs1), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons(fs1, ri, ro0), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong(fs1, ri, ro0, fi, fo, log1), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj(ri), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons(fs1, ri, ro0, fi, fo, log1), adr ∈ fs, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].size ≥ 1, ¬ adr ∈ ri2 → adr ∈ fs → adr ∈ fs, m5 = 0 → links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), asynced → boolvar0, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).trunc? ∨ inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).inode?, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode?, inodenode(inodekey(m3), md0, false, m5, 0, m6).trunc? ∨ inodenode(inodekey(m3), md0, false, m5, 0, m6).inode? ⊦ ⟨p_inode0 := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); p_inode1 := mkinode(m3, md0, false, m4, 0, m6); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs1, ri) ∧ files = abs-files(fs1, ri) ∧ orphans(abs-dirs(fs1, ri), abs-files(fs1, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).size) = p_inode0 ∧ mkinode (m3, inodenode(inodekey(m3), md0, false, m5, 0, m6).meta, inodenode(inodekey(m3), md0, false, m5, 0, m6).directory, inodenode(inodekey(m3), md0, false, m5, 0, m6).nlink, inodenode(inodekey(m3), md0, false, m5, 0, m6).nsubdirs, inodenode(inodekey(m3), md0, false, m5, 0, m6).size) = p_inode1 ∧ negdentry(mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name) = old_dent ∧ ESUCCESS = err0), fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m4 = 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr ∈ ri2

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 301:
m5 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, 0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], fs1 = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], fs2 = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, m5, 0, m6) ], key = inodekey(fs0[ri0[dentrykey(m, str)]].ino), key0 = dentrykey(m, mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', log2 = ((log0 + adr1 ') + adr2 ') + adr3 ', m3 = fs0[ri0[dentrykey(m, str)]].ino, m4 = m5 + 1, old_dent = mkdentry(str, m3), p_inode0 = mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), ri = ri2[key, adr], ri1 = ri0[inodekey(m), adr1], ri2 = ri1 -- key0, ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), ro1 = orphans(fs0, ri0), fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(m)]].directory, inodenode(inodekey(m3), md0, false, m5, 0, m6).inode?, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).inode?, fs0[ri0[inodekey(m)]].inode?, ro0.inodes?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs1, ri), file-node-cons(fs0, ri0), key-cons(key, fs[adr]), log-cons(log1, fs1), log-cons(log0, fs0), orphans-cons(fs1, ri, ro0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs1, ri, ro0, fi, fo, log1), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs1, ri, ro0, fi, fo, log1), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, adr ∈ fs, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].size ≥ 1, asynced → boolvar0, m5 = 0 → links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), ¬ adr ∈ ri2 → adr ∈ fs → adr ∈ fs, inodenode(inodekey(m3), md0, false, m5, 0, m6).trunc? ∨ inodenode(inodekey(m3), md0, false, m5, 0, m6).inode?, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).trunc? ∨ inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).inode?, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode? ⊦ ⟨p_inode1 := mkinode(m3, md0, false, m4, 0, m6); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs1, ri) ∧ files = abs-files(fs1, ri) ∧ orphans(abs-dirs(fs1, ri), abs-files(fs1, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).size) = p_inode0 ∧ mkinode (m3, inodenode(inodekey(m3), md0, false, m5, 0, m6).meta, inodenode(inodekey(m3), md0, false, m5, 0, m6).directory, inodenode(inodekey(m3), md0, false, m5, 0, m6).nlink, inodenode(inodekey(m3), md0, false, m5, 0, m6).nsubdirs, inodenode(inodekey(m3), md0, false, m5, 0, m6).size) = p_inode1 ∧ negdentry(mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name) = old_dent ∧ ESUCCESS = err0), fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m4 = 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, adr ∈ ri2, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ adr ∈ fs[adr0, nd] ↔ adr = adr0 ∨ adr ∈ fs; (ws)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ adr0 ≠ adr1 → ¬ adr0 ∈ ri[key1, adr1] -- key2; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)%⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?; (ss)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)