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Proof step 97 from proof inv-mkdir (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 98:
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), log-cons (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1)]), orphans-cons(fs1, ri1, ro), replay-cons-strong (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1)], ri1[inodekey(m), adr1], ro, fi, fo, log0 + adr1 '), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), replay-safe(log0, fs1, fi ⊖ fo), ri-cons (ri1[inodekey(m), adr1], fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1)]), 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, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro, adr2 ∈ fs1, replay-safe (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 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 + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 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 + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 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 + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 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 + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ] [adr3, inodenode(inodekey(n), md, true, 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, (ri1[inodekey(m), adr1] ⊖ ro)[dentrykey(m, str), adr2] = ri1[inodekey(m), adr1][dentrykey(m, str), adr2] ⊖ ro ∧ 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 + 1, 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 + 1, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ])

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);%⊦ replay-one(adr, dentrynode(key, ino), ri) = (ino ≠ 0 ⊃ ri[key, adr];ri -- key); (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ 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 ∈ fs[adr0, nd] ↔ adr = adr0 ∨ adr ∈ fs; (ws)% ⊦ 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)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ dentrynode(key, m).key = key; (s)