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Proof step 155 from proof refine-create (previous step)

fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), 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, adr1 = ri1[inodekey(ino)], adr2 = adr3, adr2 = ri1[inodekey(ino)], adr3 = ri1[inodekey(ino)], ino = m0, m0 = 0, mkdir (fs1[ri1[inodekey(ino)]].size, fs1[ri1[inodekey(ino)]].meta, fs1[ri1[inodekey(ino)]].nlink, fs1[ri1[inodekey(ino)]].nsubdirs, abs-children(ino, fs1, ri1)) = mkdir ((adr1 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[ri1[inodekey(ino)]]).size, (adr1 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[ri1[inodekey(ino)]]).meta, (adr1 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[ri1[inodekey(ino)]]).nlink, (adr1 = ri1[inodekey(ino)] ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[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 156:
fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), fs1[ri1[inodekey(ino)]].directory, orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), 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, ∅)]), 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]), file-node-cons(fs1, ri1), 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) ]), log-cons(log0, fs1), 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)), orphans-cons(fs1, ri1, orphans(fs1, ri1)), 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 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ri-inj(ri1), ri-inj(fi), 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 '), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(m0) ∈ ri1, ri1[inodekey(m0)] ∈ fs1, inodekey(ino) ∈ ri1, asynced0 → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = ri1[inodekey(ino)], adr1 = adr2, adr1 = adr3, adr2 = ri1[inodekey(ino)], adr2 = adr3, adr3 = ri1[inodekey(ino)], ino = m0, m0 = 0, n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m0, str) ∈ ri1, m1 = 0 ∧ m0 ≠ ROOT_INO, (dentrykey(ino, str0) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ↔ dentrykey(ino, str0) ∈ ri1) ∧ ( dentrykey(ino, str0) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] → (adr3 = (dentrykey(m0, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = (dentrykey(m0, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (dentrykey(m0, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1) ;fs1[(dentrykey(m0, str) = dentrykey(ino, str0) ⊃ adr2;ri1[dentrykey(ino, str0)])] ) ) ) .ino = fs1[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;%at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (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)