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Proof step 542 from proof refine-unlink (previous step)

m5 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), 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, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ m3, m5 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str), asynced → boolvar0, ∀ adr0, adr1, adr2. adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, m1 ≠ 0 ∨ m = ROOT_INO ⊦ m = 0, m0 = ROOT_INO, m0 = 0, m3 = 0, fs[ri[inodekey(m0)]].directory, 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 543:
m5 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), abs-dirs(fs, ri)[m] = mkdir(m4, md, m6, m7, entries), 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[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ m3, asynced → boolvar0, m5 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str), ∀ adr0, adr1, adr2. adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ m = 0, m0 = 0, m0 = ROOT_INO, m3 = 0, fs[ri[inodekey(m0)]].directory, str ∈ entries ∧ m0 = entries[str] ∧ m1 = m6 ∧ m3 = m4 ∧ m2 = m7

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, m6, m7, 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, m6, m7, entries