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Proof step 456 from proof refine-rename-new-keep-parent (previous step)

dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode0 = new_dent_inode, new_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), old_dent0 = mkdentry(str, fs[ri[dentrykey(m3, str)]].ino), old_dent1 = negdentry(str0), old_dent_inode = mkinode(fs[ri[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2), old_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), fs[ri[inodekey(m3)]].size ≠ 0, fs[ri[dentrykey(m3, str)]].dentry?, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m3)]].inode?, 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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str) ∈ ri, ri[dentrykey(m3, str)] ∈ fs, inodekey(fs[ri[dentrykey(m3, str)]].ino) ∈ ri, ri[inodekey(m3)] ∈ fs, inodekey(m3) ∈ ri, 1 ≤ fs[ri[inodekey(m3)]].size, ⌊err0⌋ , ¬ dentrykey(m3, str0) ∈ ri, boolvar1 → 1 ≤ fs[ri[inodekey(m3)]].nsubdirs, boolvar3 → boolvar0, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size, fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar3 → boolvar2) ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = old_inode ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = new_inode ∧ mkinode(fs[ri[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ mkdentry(str, fs[ri[dentrykey(m3, str)]].ino) = old_dent0 ∧ negdentry(str0) = old_dent1 ∧ err0 = err1), fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 457:
fs[ri[dentrykey(m3, str)]] = dentrynode(key, m), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode0 = new_dent_inode, new_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), old_dent0 = mkdentry(str, m), old_dent1 = negdentry(str0), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), fs[ri[dentrykey(m3, str)]].dentry?, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m3)]].inode?, 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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m3) ∈ ri, ri[inodekey(m3)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m3, str)] ∈ fs, dentrykey(m3, str) ∈ ri, 1 ≤ fs[ri[inodekey(m3)]].size, ⌊err0⌋ , boolvar3 → boolvar0, boolvar1 → 1 ≤ fs[ri[inodekey(m3)]].nsubdirs, 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 ∧ ¬ 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(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar3 → boolvar2) ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = old_inode ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = new_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ mkdentry(str, m) = old_dent0 ∧ negdentry(str0) = old_dent1 ∧ err0 = err1), fs[ri[inodekey(m3)]].size = 0, dentrykey(m3, str0) ∈ ri, fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[dentrykey(m3, str)]], key, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m3, str)]], key, m