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Proof step 481 from proof refine-rename-new-keep-parent (previous step)

fs[ri[dentrykey(m3, str)]] = dentrynode(key, m), fs[ri[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), 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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str) ∈ ri, ri[dentrykey(m3, str)] ∈ fs, inodekey(m) ∈ ri, ri[inodekey(m3)] ∈ fs, inodekey(m3) ∈ ri, 1 ≤ m6, ⌊err0⌋ , boolvar1 → 1 ≤ m5, boolvar3 → boolvar0, m4 ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ m6 = 0, dentrykey(m3, str0) ∈ ri, m4 = 0 ∧ m3 ≠ ROOT_INO, ¬ str0 ∈ abs-dirs(fs, ri)[m3].entries ∧ str ∈ abs-dirs(fs, ri)[m3].entries ∧ m = abs-dirs(fs, ri)[m3].entries[str] ∧ m4 = abs-dirs(fs, ri)[m3].nlink ∧ m6 = abs-dirs(fs, ri)[m3].size ∧ m5 = abs-dirs(fs, ri)[m3].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 482:
fs[ri[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), fs[ri[dentrykey(m3, str)]] = dentrynode(key, m), abs-dirs(fs, ri)[m3] = mkdir(m7, md, m8, m9, entries), 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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m3) ∈ ri, ri[inodekey(m3)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m3, str)] ∈ fs, dentrykey(m3, str) ∈ ri, 1 ≤ m6, ⌊err0⌋ , boolvar3 → boolvar0, boolvar1 → 1 ≤ m5, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ m6 = 0, dentrykey(m3, str0) ∈ ri, ¬ str0 ∈ entries ∧ str ∈ entries ∧ m = entries[str] ∧ m4 = m8 ∧ m6 = m7 ∧ m5 = m9, m4 = 0 ∧ m3 ≠ 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)[m3], m7, md, m8, m9, 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)[m3], m7, md, m8, m9, entries