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Proof step 1172 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ 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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-dirs seq: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri) subst: [ino, ri, fs] → [m7, ri, fs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ dentrynode(key, m).ino = m; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss) Used terms: m7, ri, fs