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Proof step 257 from proof refine-rmdir (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m4)]] = inodenode(key2, md3, true, 1, m12, m10), abs-children(m4, fs0, ri0) = ∅, dentrykeys(inodekey(m4), ri0) = ∅, ino = m, links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), fs0[ri0[inodekey(ino)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m1, md, m3, m0, abs-children(m, fs0, ri0) -- str)][m4, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), 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(m4), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), 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(m4) ∈ ri0, ri0[inodekey(m4)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced0 → boolvar0, m3 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = m4, m = 0, m4 = ROOT_INO, m4 = 0, m4 = m, mkdir(m1, md, m3, m0, abs-children(m, fs0, ri0) -- str) = mkdir ((adr3 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m4), md0, true, 0, m12, m10) ;(adr2 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m3, m0, m1);fs0[(m = ino ⊃ adr1;ri0[inodekey(ino)])]) ) ) .size, (adr3 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m4), md0, true, 0, m12, m10) ;(adr2 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m3, m0, m1);fs0[(m = ino ⊃ adr1;ri0[inodekey(ino)])]) ) ) .meta, (adr3 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m4), md0, true, 0, m12, m10) ;(adr2 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m3, m0, m1);fs0[(m = ino ⊃ adr1;ri0[inodekey(ino)])]) ) ) .nlink, (adr3 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m4), md0, true, 0, m12, m10) ;(adr2 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m3, m0, m1);fs0[(m = ino ⊃ adr1;ri0[inodekey(ino)])]) ) ) .nsubdirs, abs-children (ino, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3])), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, m3 = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s)% ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ str ∈ entries -- str0 ↔ str ≠ str0 ∧ str ∈ entries; (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)