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Proof step 12 from proof abs-dirs-del-orphans (previous step)

fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri, ino ∈ abs-dirs(fs, ri), fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ abs-dirs(fs, ri)[ino] = 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 ⊖ orphans(fs, ri))), ino ∈ abs-keys(orphans(fs, ri)), fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: at-dirs: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri);%dir: ⊦ 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));%D-inj: ⊦ mkdir(n0, md0, m0, m1, entries0) = mkdir(n1, md1, m2, m3, entries1) ↔ ¬(md0 ≠ md1 ∨ n0 ≠ n1 ∨ m0 ≠ m2 ∨ m1 ≠ m3 ∨ entries0 ≠ entries1);%C-ext: ⊦ entries = abs-children(ino, fs, ri) ↔ (∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ ( str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino));%in-children: ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri;%at-children: ⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino;%in-dirs: ⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory;%abs-keys: ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks;% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)