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Proof step 502 from proof refine-rmdir (previous step)

fs[ri[inodekey(m0)]] = inodenode(key1, md2, true, 1, m5, m6), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), abs-dirs(fs, ri)[m] = mkdir(m4, md, m7, m8, entries), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, links(m0, fs, ri) = ∅ ++ dentrykey(m, str), fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, ri[dentrykey(m, str)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ m3, 1 ≤ m2, ⌊err0⌋ , asynced → boolvar0, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ m = 0, m0 = ROOT_INO, m0 = 0, m2 = 0, m3 = 0, str ∈ entries ∧ m0 = entries[str] ∧ m1 = m7 ∧ m3 = m4 ∧ m2 = m8 ∧ fs[ri[inodekey(entries[str])]].directory ∧ 1 = fs[ri[inodekey(entries[str])]].nlink ∧ m6 = fs[ri[inodekey(entries[str])]].size ∧ m5 = fs[ri[inodekey(entries[str])]].nsubdirs, m1 = 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, ri, fs] 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)% ⊦ 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, ri, fs