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Proof step 89 from proof inv-create (previous step)

fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs1, ri1, ro, fi, fo, log0), inodekey(m) ∈ ri1, ri1[inodekey(m)] ∈ fs1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, n = 0, replay-cons-strong (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m), adr1][dentrykey(m, str), adr2][inodekey(n), adr3], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro, inodenode(inodekey(n), md, false, 1, 0, 0).key = inodekey(n) ∧ ¬ adr3 ∈ fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] ∧ log-cons ((log0 + adr1 ') + adr2 ', fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]) ∧ node-cons(inodekey(n), inodenode(inodekey(n), md, false, 1, 0, 0)) ∧ ri-cons (ri1[inodekey(m), adr1][dentrykey(m, str), adr2], fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]) ∧ replay-cons-strong (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ], ri1[inodekey(m), adr1][dentrykey(m, str), adr2], ro, fi, fo, (log0 + adr1 ') + adr2 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
replay-log(log0, fs1, fi ⊖ fo) = ri1 ⊖ ro, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), replay-safe(log0, fs1, fi ⊖ fo), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs1, ri1, ro, fi, fo, log0), inodekey(m) ∈ ri1, ri1[inodekey(m)] ∈ fs1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro, replay-cons-strong (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ], ri1[inodekey(m), adr1][dentrykey(m, str), adr2], ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ ri-cons (ri1[inodekey(m), adr1][dentrykey(m, str), adr2], fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]) ∧ log-cons (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]), replay-safe (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], fi ⊖ fo) [inodekey(m), adr1 ] ∧ ¬ adr3 ∈ replay-log (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], fi ⊖ fo) [inodekey(m), adr1 ] [dentrykey(m, str), adr2 ] ∧ replay-log (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], fi ⊖ fo) [inodekey(m), adr1 ] [dentrykey(m, str), adr2 ] [inodekey(n), adr3 ] = ri1[inodekey(m), adr1][dentrykey(m, str), adr2][inodekey(n), adr3] ⊖ ro

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ 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, 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)%⊦ 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)% ⊦ 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)