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Proof step 1171 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ fs[ri[inodekey(m3)]].directory ↔ ¬ fs[ri[inodekey(m)]].directory, fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m3), fs[ri[dentrykey(m7, str)]] = dentrynode(key, m), fs[ri[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), 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(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, inodekey(m3) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[dentrykey(m7, str)] ∈ fs, dentrykey(m7, str) ∈ ri, ⌊err0⌋ , fs[ri[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri) = ∅, fs[ri[inodekey(m3)]].directory → abs-children(m3, fs, ri) = ∅, boolvar3 → boolvar4, m10 = 0 → links(m3, fs, ri) = ∅ ++ dentrykey(m7, str0), fs[ri[inodekey(m3)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m6 = fs[ri[inodekey(m3)]].size ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = 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 ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∨ fs[ri[inodekey(m3)]].directory ∧ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ m6 = fs[ri[inodekey(m3)]].size, ¬ 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(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m7 = ROOT_INO ⊦ m3 = ROOT_INO, m3 = 0, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), m4 = 0 ∧ m7 ≠ ROOT_INO, str0 ∈ abs-dirs(fs, ri)[m7].entries ∧ m3 = abs-dirs(fs, ri)[m7].entries[str0] ∧ ( fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].directory ∧ m10 + 1 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nlink ∧ m6 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].size ∧ m5 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].directory ∧ m10 + 1 = fs[ri[inodekey(abs-dirs(fs, ri)[m7].entries[str0])]].nlink ∧ m5 = 0 ∧ ¬ boolvar2) ∧ str ∈ abs-dirs(fs, ri)[m7].entries ∧ m = abs-dirs(fs, ri)[m7].entries[str] ∧ m4 = abs-dirs(fs, ri)[m7].nlink ∧ m11 + 1 = abs-dirs(fs, ri)[m7].size ∧ n0 + (boolvar1 ⊃ 1;0) = abs-dirs(fs, ri)[m7].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1172:
¬ fs[ri[inodekey(m3)]].directory ↔ ¬ fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs[ri[dentrykey(m7, str)]] = dentrynode(key, m), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m3), abs-dirs(fs, ri)[m7] = mkdir(m8, md, m9, m12, 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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m7, str) ∈ ri, ri[dentrykey(m7, str)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m) ∈ ri, inodekey(m3) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, dentrykey(m7, str0) ∈ ri, ⌊err0⌋ , m10 = 0 → links(m3, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar3 → boolvar4, fs[ri[inodekey(m3)]].directory → abs-children(m3, fs, ri) = ∅, fs[ri[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri) = ∅, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = 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 ∧ ¬ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∨ fs[ri[inodekey(m3)]].directory ∧ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ m6 = fs[ri[inodekey(m3)]].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, fs[ri[inodekey(m3)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m6 = fs[ri[inodekey(m3)]].size ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2 ⊦ m3 = 0, m3 = ROOT_INO, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), str0 ∈ entries ∧ m3 = entries[str0] ∧ ( fs[ri[inodekey(entries[str0])]].directory ∧ m10 + 1 = fs[ri[inodekey(entries[str0])]].nlink ∧ m6 = fs[ri[inodekey(entries[str0])]].size ∧ m5 = fs[ri[inodekey(entries[str0])]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(entries[str0])]].directory ∧ m10 + 1 = fs[ri[inodekey(entries[str0])]].nlink ∧ m5 = 0 ∧ ¬ boolvar2) ∧ str ∈ entries ∧ m = entries[str] ∧ m4 = m9 ∧ m11 + 1 = m8 ∧ n0 + (boolvar1 ⊃ 1;0) = m12, m4 = 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)[m7], m8, md, m9, 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)[m7], m8, md, m9, m12, entries