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Proof step 15 from proof abs-dirs-del-orphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [dentrykey(ino, str), 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)% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ ¬ dentrykey(m, str).data?; (s) Used terms: dentrykey(ino, str), orphans(fs, ri), ri