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Proof step 96 from proof inv-mkdir (previous step)

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 + 1, 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 + 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-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)] [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 + 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) ]), ((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 + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ))

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: inodekey(m) = key

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → key-cons(key, fs[ri[key]]); (ss)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s) Used formulas: inodekey(m) = key