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Proof step 140 from proof refine-mkdir (previous step)

abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])][ino] = mkdir(m, md0, m3, m4, entries), fs1[ri1[inodekey(ino)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [ino, mkdir(m, md2, m3, m4, entries) ], 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, m1, 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, m1, 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, m1, 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, m1, 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, m1, 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 '), ri1[inodekey(ino)] ∈ fs1, inodekey(ino) ∈ ri1, ino ∈ abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])], asynced0 → boolvar0, m1 ≠ 0 ∨ ino = ROOT_INO, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO ⊦ adr1 = adr3, adr2 = adr1, adr2 = adr3, ino = 0, ino = n, mkdir(m, md2, m3, m4, entries) = mkdir (m6 + 1, md2, m1, m2 + 1, abs-children (ino, fs1[adr1, inodenode(inodekey(ino), md2, true, m1, 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])), n = 0, dentrykey(ino, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, n ∈ abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])], m1 = 0 ∧ ino ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
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 '), ri1[inodekey(ino)] ∈ fs1, inodekey(ino) ∈ ri1, asynced0 → boolvar0, m3 ≠ 0 ∨ ino = ROOT_INO, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO ⊦ adr1 = adr3, adr2 = adr1, adr2 = adr3, n = 0, dentrykey(ino, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m3 = 0 ∧ ino ≠ ROOT_INO, (str = str0 ∨ dentrykey(ino, str0) ∈ ri1 ↔ dentrykey(ino, str0) ∈ ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]) ∧ ( str = str0 ∨ dentrykey(ino, str0) ∈ ri1 → abs-children(ino, fs1, ri1)[str, n][str0] = (adr3 = (dentrykey(ino, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (dentrykey(ino, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ dentrynode(dentrykey(ino, str), n) ;(adr1 = (dentrykey(ino, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ inodenode(inodekey(ino), md2, true, m3, m2 + 1, m6 + 1) ;fs1[(dentrykey(ino, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)])] ) ) ) .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)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ ino ∈ dirs → ino ≠ 0; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)