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Proof step 370 from proof refine-rmdir (previous step)

1 = fs0[ri0[inodekey(m2)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md2, true, 1, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size), abs-dirs(fs0, ri0)[m] = mkdir(m4, md3, m5, m6, entries), abs-children(m2, fs0, ri0) = ∅, dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m, str), fs0[ri0[inodekey(m2)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ]), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2)), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2), 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(m2), 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(m2), md0, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m2), adr3], orphans(fs0, ri0) ++ inodekey(m2), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m2) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced → boolvar0, m3 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m2 = 0, m2 = ROOT_INO, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, str ∈ entries ∧ m2 = entries[str] ∧ m3 = m5 ∧ m1 + 1 = m4 ∧ m0 + 1 = m6, m3 = 0 ∧ m ≠ ROOT_INO

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-dirs seq: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri) subst: [ino, ri, fs] → [m, ri0, fs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ dentrynode(key, m).ino = m; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss) Used terms: m, ri0, fs0