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Proof step 226 from proof refine-rmdir (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m)]] = inodenode(key2, md6, true, 1, m12 + 1, m10 + 1), abs-children(m, fs0, ri0) = ∅, dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m, str), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(ino) ∈ ri0, asynced0 → boolvar0 ⊦ # links(m, abs-dirs(fs0, ri0)) = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = m, links(m, abs-dirs(fs0, ri0)) = ∅, m = ROOT_INO, m = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3] ∧ (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .directory) ∧ ( fs0[ri0[inodekey(ino)]].directory → mkdir (fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, fs0[ri0[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri0)) = mkdir ((adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .size, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .meta, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .nlink, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .nsubdirs, abs-children (ino, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3])))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 227:
fs0[ri0[inodekey(m)]] = inodenode(key2, md6, true, 1, m12 + 1, m10 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m), abs-children(m, fs0, ri0) = ∅, dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m, str), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(ino) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, asynced0 → boolvar0 ⊦ # links(m, abs-dirs(fs0, ri0)) = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = m, inodekey(ino) = inodekey(m), links(m, abs-dirs(fs0, ri0)) = ∅, m = 0, m = ROOT_INO, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, ( fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3] ∧ (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .directory) ∧ ( fs0[ri0[inodekey(ino)]].directory → mkdir (fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, fs0[ri0[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri0)) = mkdir ((adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .size, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .meta, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .nlink, (adr3 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ;(adr2 = ri0[inodekey(ino)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, 1, m12, m10);fs0[ri0[inodekey(ino)]]) ) ) .nsubdirs, abs-children (ino, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3])))

Rule argument

fma: inodekey(ino) = inodekey(m)

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s) Used formulas: inodekey(ino) = inodekey(m)