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Proof step 501 from proof refine-rmdir (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 502:
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

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs, ri)[m], m4, md, m7, m8, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs, ri)[m], m4, md, m7, m8, entries