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Proof step 1466 from proof refine-rename-overwrite-reparent-dir (previous step)

abs-dirs(fs, ri)[m7] = mkdir(m18, md0, m19, m20, entries0), 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-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, 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, inodekey(m11) ∈ 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, m4 = 0 ∧ m11 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ ROOT_INO, str0 ∈ entries0 ∧ m0 = entries0[str0] ∧ fs[ri[inodekey(entries0[str0])]].directory ∧ m14 + 1 = fs[ri[inodekey(entries0[str0])]].nlink ∧ m12 = fs[ri[inodekey(entries0[str0])]].size ∧ m10 = fs[ri[inodekey(entries0[str0])]].nsubdirs ∧ m5 = m19 ∧ m8 = m18 ∧ m6 = m20

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)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ dentrynode(key, m).ino = m; (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%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss) Used terms: m7, ri, fs