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Proof step 151 from proof refine-mkdir (previous step)

fs1[ri1[inodekey(ino)]] = inodenode(key0, md1, true, m3, m2, m6), orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), afs-cons ((abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m3, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [ino, mkdir(m6 + 1, md2, m3, m2 + 1, abs-children(ino, fs1, ri1)[str, n]) ], abs-files(fs1, ri1)), file-node-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), file-node-cons(fs1, ri1), log-cons (log0, fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), log-cons(log0, fs1), orphans-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), ri-inj(ri1), ri-inj(fi), ubifs-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(ino) ∈ ri1, ri1[inodekey(ino)] ∈ fs1, dentrykey(ino, str0) ∈ ri1, asynced0 → boolvar0, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO, m3 ≠ 0 ∨ ino = ROOT_INO ⊦ fs1[ri1[dentrykey(ino, str0)]].ino = (adr2 = ri1[dentrykey(ino, str0)] ⊃ dentrynode(dentrykey(ino, str), n) ;(adr1 = ri1[dentrykey(ino, str0)] ⊃ inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1);fs1[ri1[dentrykey(ino, str0)]]) ) .ino, adr1 = adr3, adr2 = adr3, adr2 = adr1, adr3 = ri1[dentrykey(ino, str0)], dentrykey(ino, str) = dentrykey(ino, str0), n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(ino, str) ∈ ri1, m3 = 0 ∧ ino ≠ ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 152:
fs1[ri1[inodekey(ino)]] = inodenode(key0, md1, true, m3, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m3, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [ino, mkdir(m6 + 1, md2, m3, m2 + 1, abs-children(ino, fs1, ri1)[str, n]) ], abs-files(fs1, ri1)), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), replay-cons-strong (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), dentrykey(ino, str0) ∈ ri1, ri1[inodekey(ino)] ∈ fs1, inodekey(ino) ∈ ri1, asynced0 → boolvar0, m3 ≠ 0 ∨ ino = ROOT_INO, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO ⊦ fs1[ri1[dentrykey(ino, str0)]].ino = (adr2 = ri1[dentrykey(ino, str0)] ⊃ dentrynode(dentrykey(ino, str), n) ;(adr1 = ri1[dentrykey(ino, str0)] ⊃ inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1);fs1[ri1[dentrykey(ino, str0)]]) ) .ino, adr1 = adr3, adr2 = adr1, adr2 = adr3, adr2 = ri1[dentrykey(ino, str0)], adr3 = ri1[dentrykey(ino, str0)], dentrykey(ino, str) = dentrykey(ino, str0), n = 0, dentrykey(ino, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m3 = 0 ∧ ino ≠ ROOT_INO

Rule argument

fma: adr2 = ri1[dentrykey(ino, str0)]

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ dentrynode(key, m).ino = m; (s)% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss) Used formulas: adr2 = ri1[dentrykey(ino, str0)]