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Proof step 393 from proof inv-rename-overwrite-reparent (previous step)

m11 + 1 = fs0[ri0[inodekey(m8)]].nlink, ¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, 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), 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(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) = ∅, 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, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size ⊦ 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, m11 = 0, m8 = ROOT_INO, m8 = 0, replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5], ro, fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 394:
m11 + 1 = fs0[ri0[inodekey(m8)]].nlink, ¬ fs0[ri0[inodekey(m8)]].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), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), 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 ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, ¬ 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 ⊦ 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, m11 = 0, 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], replay-safe (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) ∧ ¬ adr3 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) ∧ ¬ adr4 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] ∧ ¬ adr5 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] ∧ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] [inodekey(m8), adr5 ] = (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5] ⊖ ro

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ replay-log(adr ', fs, ri) = replay-one(adr, fs[adr], ri); (s)%⊦ replay-log(adr ' + log, fs, ri) = replay-log(log, fs, replay-one(adr, fs[adr], ri)); (s)%⊦ replay(ax0 + ax1, fs, fi, fo) = replay-log(ax1, fs, replay(ax0, fs, fi, fo)); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ replay-safe(adr ', fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]); (s)%⊦ replay-one(adr, inodenode(key, md, boolvar, n, n0, m), ri) = (n ≠ 0 ∨ key.ino = ROOT_INO ⊃ ri[key, adr] ;(boolvar ⊃ ri -- key;ri ⊖ key) ); (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)%⊦ replay-one(adr, dentrynode(key, ino), ri) = (ino ≠ 0 ⊃ ri[key, adr];ri -- key); (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)%⊦ replay-safe(adr ' + log, fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]) ∧ replay-safe(log, fs, replay-one(adr, fs[adr], ri)); (s)%⊦ replay-safe(log0 + log1, fs, ri) ↔ replay-safe(log0, fs, ri) ∧ replay-safe(log1, fs, replay-log(log0, fs, ri)); (s)% ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)%⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) → ( replay-cons-strong(fs0, ri0, ro0, fi0, fo0, log0) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro → replay-safe(log0, fs0, fi0 ⊖ fo0) ∧ replay(log0, fs0, fi0, fo0) = ri0 ⊖ ro0); (ss)