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

¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, 1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m5)]].size, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, adr = adr2 ∨ adr = adr3 ∨ adr = adr4 ∨ adr = adr5 ⊦ adr = adr1, 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, m8 = ROOT_INO, m8 = 0, adr ∈ log0, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], (adr = adr5 ∨ adr = adr4 ∨ adr = adr3 ∨ adr = adr2 ∨ adr ∈ fs0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .inode? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .inode? ∧ (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .ino ≠ 0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .dentry? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .dentry?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .data? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .data?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .trunc? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .inode?)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 173:
¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, 1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, adr = adr2 ∨ adr = adr3 ∨ adr = adr4 ∨ adr = adr5, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m5)]].size ⊦ adr = adr1, adr = adr2, 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, m8 = 0, m8 = ROOT_INO, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr ∈ log0, (adr = adr5 ∨ adr = adr4 ∨ adr = adr3 ∨ adr = adr2 ∨ adr ∈ fs0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .inode? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .inode? ∧ (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .ino ≠ 0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .dentry? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .dentry?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .data? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .data?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .trunc? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1);(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);fs0[adr])) ) ) .key .inode?)

Rule argument

fma: adr = adr2

Additional information

Used simplifier rules: ⊦ ¬ dentrynode(key, m).inode?; (s)% ⊦ dentrynode(key, m).dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrynode(key, m).data?; (s)% ⊦ ¬ dentrynode(key, m).trunc?; (s) Used formulas: adr = adr2