[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 726 from proof refine-rename-overwrite-reparent-dir (previous step)

boolvar ↔ boolvar1, fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, m14 + 1, m6, m8), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), abs-children(m0, fs0, ri0) = ∅, adr = adr5, dentrykeys(inodekey(m0), ri0) = ∅, fs = fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, m6, m8) ], fs1 = fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, m6, m8) ], key = inodekey(mkdentry(str0, m0).ino), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', log1 = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', nd = inodenode(inodekey(mkdentry(str0, m0).ino), md0, true, m14, m6, m8), new_dent = mkdentry(str0, m0), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), mkdentry(str, m).dentry?, mkdentry(str0, m0).dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, inodenode(inodekey(m11), md2, true, m4, m16, m13).inode?, nd.inode?, orphans(fs0, ri0).inodes?, fo.inodes?, ro0.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons(fs, ri), key-cons(key, fs1[adr]), log-cons(log0, fs0), log-cons(log, fs), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons(fs, ri, ro0), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong(fs, ri, ro0, fi, fo, log), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons(fs, ri, ro0, fi, fo, log), ri0[inodekey(m)] ∈ fs0, dentrykey(m7, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(m11) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, adr ∈ fs1, m14 = 0 → links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode?, inodenode(inodekey(m11), md2, true, m4, m16, m13).trunc? ∨ inodenode(inodekey(m11), md2, true, m4, m16, m13).inode?, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO, nd.trunc? ∨ nd.inode? ⊦ ⟨old_dent_inode := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); new_dent_inode := mkinode(m0, md0, true, m14 + 1, m6, m8); new_inode := mkinode(m7, md1, true, m1, m2, m3); old_inode := mkinode(m11, md2, true, m4, m16 + 1, m13 + 1); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar2 → boolvar1) ∧ mkinode (m11, inodenode(inodekey(m11), md2, true, m4, m16, m13).meta, inodenode(inodekey(m11), md2, true, m4, m16, m13).directory, inodenode(inodekey(m11), md2, true, m4, m16, m13).nlink, inodenode(inodekey(m11), md2, true, m4, m16, m13).nsubdirs, inodenode(inodekey(m11), md2, true, m4, m16, m13).size) = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) = old_dent_inode ∧ mkinode(m0, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size) = new_dent_inode ∧ negdentry(str) = old_dent0 ∧ mkdentry(new_dent.name, mkdentry(str, m).ino) = old_dent1 ∧ ESUCCESS = err0), nd.nlink = 0, adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, adr ∈ ri1, adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m11, str), adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], m4 = 0 ∧ m11 ≠ ROOT_INO, m1 = 0 ∧ m7 ≠ ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 727:
boolvar ↔ boolvar1, fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, m14 + 1, m6, m8), abs-children(m0, fs0, ri0) = ∅, adr = adr5, dentrykeys(inodekey(m0), ri0) = ∅, fs = fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, m6, m8) ], fs1 = fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, m6, m8) ], key = inodekey(mkdentry(str0, m0).ino), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', log1 = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', nd = inodenode(inodekey(mkdentry(str0, m0).ino), md0, true, m14, m6, m8), new_dent = mkdentry(str0, m0), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), mkdentry(str0, m0).dentry?, mkdentry(str, m).dentry?, fs0[ri0[inodekey(m)]].directory, nd.inode?, inodenode(inodekey(m11), md2, true, m4, m16, m13).inode?, fs0[ri0[inodekey(m)]].inode?, ro0.inodes?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs, ri), file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log, fs), log-cons(log0, fs0), orphans-cons(fs, ri, ro0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs, ri, ro0, fi, fo, log), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs, ri, ro0, fi, fo, log), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), adr ∈ fs1, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m11) ∈ ri0, inodekey(m7) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m7, str0) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, boolvar2 → boolvar0, m14 = 0 → links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), nd.trunc? ∨ nd.inode?, m4 ≠ 0 ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, inodenode(inodekey(m11), md2, true, m4, m16, m13).trunc? ∨ inodenode(inodekey(m11), md2, true, m4, m16, m13).inode?, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode? ⊦ ⟨new_dent_inode := mkinode(m0, md0, true, m14 + 1, m6, m8); new_inode := mkinode(m7, md1, true, m1, m2, m3); old_inode := mkinode(m11, md2, true, m4, m16 + 1, m13 + 1); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar2 → boolvar1) ∧ mkinode (m11, inodenode(inodekey(m11), md2, true, m4, m16, m13).meta, inodenode(inodekey(m11), md2, true, m4, m16, m13).directory, inodenode(inodekey(m11), md2, true, m4, m16, m13).nlink, inodenode(inodekey(m11), md2, true, m4, m16, m13).nsubdirs, inodenode(inodekey(m11), md2, true, m4, m16, m13).size) = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) = old_dent_inode ∧ mkinode(m0, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size) = new_dent_inode ∧ negdentry(str) = old_dent0 ∧ mkdentry(new_dent.name, mkdentry(str, m).ino) = old_dent1 ∧ ESUCCESS = err0), nd.nlink = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m0 = ROOT_INO, m0 = 0, m11 = m7, m11 = 0, m7 = 0, adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], adr2 ∈ ri0 -- dentrykey(m11, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr ∈ ri1, m1 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (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)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (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)%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)% ⊦ mkdentry(str, m).dentry?; (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)