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Proof step 1461 from proof refine-rename-overwrite-reparent-dir (previous step)

fs[ri[inodekey(m7)]] = inodenode(key3, md5, true, m5, m6, m8), fs[ri[inodekey(m)]] = inodenode(key1, md3, true, m1, m2, m3), fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs[ri[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs[ri[inodekey(m0)]] = inodenode(key4, md6, true, m14 + 1, m10, m12), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, 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), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, ri[dentrykey(m7, str0)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[inodekey(m11)] ∈ fs, inodekey(m11) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, dentrykey(m11, str) ∈ ri, ⌊err0⌋ , boolvar2 → boolvar0, m14 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m7, str0), m4 ≠ 0 ∨ m11 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ m0 = ROOT_INO, m0 = 0, m11 = m7, m11 = 0, m7 = 0, m5 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO, str0 ∈ abs-dirs(fs, ri)[m7].entries ∧ m0 = abs-dirs(fs, ri)[m7].entries[str0] ∧ fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].directory ∧ m14 + 1 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nlink ∧ m12 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].size ∧ m10 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nsubdirs ∧ fs[ri[inodekey(abs-dirs(fs, ri)[m11].entries[str])]].directory ∧ str ∈ abs-dirs(fs, ri)[m11].entries ∧ m = abs-dirs(fs, ri)[m11].entries[str] ∧ m4 = abs-dirs(fs, ri)[m11].nlink ∧ m13 + 1 = abs-dirs(fs, ri)[m11].size ∧ m16 + 1 = abs-dirs(fs, ri)[m11].nsubdirs ∧ m5 = abs-dirs(fs, ri)[m7].nlink ∧ m8 = abs-dirs(fs, ri)[m7].size ∧ m6 = abs-dirs(fs, ri)[m7].nsubdirs ∧ m1 = fs[ri[inodekey(abs-dirs(fs, ri)[m11].entries[str])]].nlink ∧ m3 = fs[ri[inodekey(abs-dirs(fs, ri)[m11].entries[str])]].size ∧ m2 = fs[ri[inodekey(abs-dirs(fs, ri)[m11].entries[str])]].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1462:
fs[ri[inodekey(m0)]] = inodenode(key4, md6, true, m14 + 1, m10, m12), fs[ri[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), fs[ri[inodekey(m)]] = inodenode(key1, md3, true, m1, m2, m3), fs[ri[inodekey(m7)]] = inodenode(key3, md5, true, m5, m6, m8), abs-dirs(fs, ri)[m11] = mkdir(m9, md, m15, m17, entries), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, 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), dentrykey(m11, str) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, inodekey(m11) ∈ ri, ri[inodekey(m11)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , m14 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, str0 ∈ abs-dirs(fs, ri)[m7].entries ∧ m0 = abs-dirs(fs, ri)[m7].entries[str0] ∧ fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].directory ∧ m14 + 1 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nlink ∧ m12 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].size ∧ m10 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nsubdirs ∧ fs[ri[inodekey(entries[str])]].directory ∧ str ∈ entries ∧ m = entries[str] ∧ m4 = m15 ∧ m13 + 1 = m9 ∧ m16 + 1 = m17 ∧ m5 = abs-dirs(fs, ri)[m7].nlink ∧ m8 = abs-dirs(fs, ri)[m7].size ∧ m6 = abs-dirs(fs, ri)[m7].nsubdirs ∧ m1 = fs[ri[inodekey(entries[str])]].nlink ∧ m3 = fs[ri[inodekey(entries[str])]].size ∧ m2 = fs[ri[inodekey(entries[str])]].nsubdirs, m4 = 0 ∧ m11 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ 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)[m11], m9, md, m15, m17, 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)[m11], m9, md, m15, m17, entries