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Proof step 7 from proof abs-files-orphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Diff-get seq: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key] subst: [key, ks, ri] → [inodekey(ino), orphans(fs, ri), ri] 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)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s) Used terms: inodekey(ino), orphans(fs, ri), ri