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Proof step 18 from proof abs-files-del-orphans (previous step)

datakey(ino, n) ∈ ri, inodekey(ino) ∈ ri, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs[ri[inodekey(ino)]].directory, datakey(ino, n) ∈ ri ⊖ orphans(fs, ri), fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: in-dels-ro seq: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks) subst: [ks, ri, key] → [orphans(fs, ri), ri, datakey(ino, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s) Used terms: orphans(fs, ri), ri, datakey(ino, n)