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Proof step 95 from proof inv-create (previous step)

inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1).key = inodekey(m), 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[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)]), log-cons(log0, fs1), node-cons(inodekey(m), inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), replay-safe(log0, fs1, fi ⊖ fo), ri-cons(ri1, fs1), 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, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro, adr1 ∈ fs1, replay-one (adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1), ri1 ⊖ ro) = ri1[inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1).key, adr1] ⊖ ro ∧ ri-cons (ri1[inodekey(m), adr1], fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)]), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
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), key-cons(key, fs1[ri1[key]]), log-cons(log0, fs1), 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)]), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), replay-safe(log0, fs1, fi ⊖ fo), ri-cons(ri1, fs1), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, key ∈ ri1, ri1[key] ∈ fs1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, n = 0, adr1 ∈ fs1, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr2 ∈ fs1, adr3 ∈ fs1, 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, 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) ]), ((inodekey(m) = key ⊃ adr1;ri1[key]) = adr1 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) ∈ fs1) ∧ key-cons (key, (adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ))

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%⊦ ri-cons(ri, fs) → ( ri-cons(ri0, fs0) ↔ (∀ key. (key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) → key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]]))); (ss)% ⊦ ¬ key ∈ ro → (ri ⊖ ro) -- key = (ri -- key) ⊖ ro; (s)%⊦ ¬ inodekey(ino) ∈ ro → (ri ⊖ ro)[inodekey(ino), adr] = ri[inodekey(ino), adr] ⊖ ro; (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)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)