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Proof step 135 from proof refine-create (previous step)

fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), ino = m0, fs1[ri1[inodekey(ino)]].directory, fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md2, m1, m2, abs-children(m0, fs1, ri1)[str, n])], (abs-files(fs1, ri1) ++ n)[n, mkfile(0, md, 1, ∅)]), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, 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(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(ino) ∈ ri1, ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced0 → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, mkdir(m6 + 1, md2, m1, m2, abs-children(m0, fs1, ri1)[str, n]) = mkdir ((adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])]) ) ) .size, (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])]) ) ) .meta, (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])]) ) ) .nlink, (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])]) ) ) .nsubdirs, abs-children (ino, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3])), n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m1 = 0 ∧ m0 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md2, m1, m2, abs-children(m0, fs1, ri1)[str, n])], (abs-files(fs1, ri1) ++ n)[n, mkfile(0, md, 1, ∅)]), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, 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(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced0 → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, (str = str0 ∨ dentrykey(m0, str0) ∈ ri1 ↔ dentrykey(m0, str0) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]) ∧ ( str = str0 ∨ dentrykey(m0, str0) ∈ ri1 → abs-children(m0, fs1, ri1)[str, n][str0] = (adr3 = (dentrykey(m0, str) = dentrykey(m0, str0) ⊃ adr2;ri1[dentrykey(m0, str0)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (dentrykey(m0, str) = dentrykey(m0, str0) ⊃ adr2;ri1[dentrykey(m0, str0)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (dentrykey(m0, str) = dentrykey(m0, str0) ⊃ adr2;ri1[dentrykey(m0, str0)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1) ;fs1[(dentrykey(m0, str) = dentrykey(m0, str0) ⊃ adr2;ri1[dentrykey(m0, str0)])] ) ) ) .ino), m1 = 0 ∧ m0 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: mkdir-inj: ⊦ mkdir(n, md, m, n0, entries0) = mkdir(n, md, m, n0, entries1) ↔ entries0 = entries1;%in-insert: ⊦ str ∈ entries[str0, n] ↔ str0 = str ∨ str ∈ entries;%at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ entries = abs-children(ino, fs, ri) ↔ (∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ ( str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino)); (ss)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)