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Proof step 530 from proof refine-rename-overwrite-keep-parent-identity (previous step)

fs[ri[dentrykey(m6, str)]] = dentrynode(key, m), fs[ri[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), 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(m6, str) ∈ ri, ri[dentrykey(m6, str)] ∈ fs, inodekey(m) ∈ ri, ri[inodekey(m6)] ∈ fs, inodekey(m6) ∈ ri, 1 ≤ m9, ⌊err0⌋ , fs[ri[inodekey(m)]].directory → dentrykeys(inodekey(m), ri) = ∅, fs[ri[inodekey(m)]].directory → abs-children(m, fs, ri) = ∅, boolvar4 → boolvar1, m0 = 1 → links(m, fs, ri) = ∅ ++ dentrykey(m6, str), boolvar2 → 1 ≤ m8, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3, fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m5 = fs[ri[inodekey(m)]].size ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ m5 = fs[ri[inodekey(m)]].size, links(m6, abs-dirs(fs, ri)) ≠ ∅ ∨ m6 = ROOT_INO, m7 ≠ 0 ∨ m6 = ROOT_INO ⊦ m = 0, m = ROOT_INO, m0 = 0, m6 = 0, m9 = 0, m7 = 0 ∧ m6 ≠ ROOT_INO, str ∈ abs-dirs(fs, ri)[m6].entries ∧ m = abs-dirs(fs, ri)[m6].entries[str] ∧ m7 = abs-dirs(fs, ri)[m6].nlink ∧ m9 = abs-dirs(fs, ri)[m6].size ∧ m8 = abs-dirs(fs, ri)[m6].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 531:
fs[ri[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs[ri[dentrykey(m6, str)]] = dentrynode(key, m), abs-dirs(fs, ri)[m6] = mkdir(m10, md, m11, m12, 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(m6) ∈ ri, ri[inodekey(m6)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m6, str)] ∈ fs, dentrykey(m6, str) ∈ ri, 1 ≤ m9, ⌊err0⌋ , boolvar2 → 1 ≤ m8, m0 = 1 → links(m, fs, ri) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, fs[ri[inodekey(m)]].directory → abs-children(m, fs, ri) = ∅, fs[ri[inodekey(m)]].directory → dentrykeys(inodekey(m), ri) = ∅, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs, ri)) ≠ ∅ ∨ m6 = ROOT_INO, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ m5 = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m5 = fs[ri[inodekey(m)]].size ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3 ⊦ m = ROOT_INO, m = 0, m0 = 0, m6 = 0, m9 = 0, str ∈ entries ∧ m = entries[str] ∧ m7 = m11 ∧ m9 = m10 ∧ m8 = m12, m7 = 0 ∧ m6 ≠ 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)[m6], m10, md, m11, m12, 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)[m6], m10, md, m11, m12, entries