[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 511 from proof inv-rename-overwrite-reparent (previous step)

n0 + (boolvar3 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, m1 + 1 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), adr = adr2, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(fs0[ri0[dentrykey(m0, str0)]].ino), md2, boolvar1, m11, m6, m7) ], key = dentrykey(m0, mkdentry(str0, fs0[ri0[dentrykey(m0, str0)]].ino).name), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', ri = ri0 -- dentrykey(m, str), fs0[ri0[dentrykey(m0, str0)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m0, str0)]].ino) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str0)]].ino), ri0) = ∅, m11 = 0 → links(fs0[ri0[dentrykey(m0, str0)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str0), ¬ adr ∈ ri → adr ∈ fs → adr ∈ fs, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, m9 ≠ 0 ∨ m0 = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ fs0[ri0[dentrykey(m0, str0)]].ino = ROOT_INO, fs0[ri0[dentrykey(m0, str0)]].ino = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m = 0, m0 = m, m0 = 0, adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 512:
m1 + 1 = fs0[ri0[inodekey(m)]].size, n0 + (boolvar3 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[dentrykey(m0, str0)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str0)]].ino) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), m11 = 0 → links(fs0[ri0[dentrykey(m0, str0)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str0), fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str0)]].ino), ri0) = ∅, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri0[inodekey(m5)]].nlink ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str0)]].ino)]].size ⊦ fs0[ri0[dentrykey(m0, str0)]].ino = 0, fs0[ri0[dentrykey(m0, str0)]].ino = ROOT_INO, adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m = 0, m0 = 0, m0 = m, inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ dentrynode(key, m).key = key; (s)% ⊦ dentrynode(key, m).dentry?; (s)%⊦ key-cons(dentrykey(ino, str), nd) ↔ nd.dentry? ∧ nd.key = dentrykey(ino, str); (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)