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Proof step 4 from proof abs-dirs-del-orphans (previous step)

inodekey(ino) ∈ ri ⊦ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO → (fs[ri[inodekey(ino)]].directory ↔ fs[(ri ⊖ orphans(fs, ri))[inodekey(ino)]].directory)) ∧ ( fs[ri[inodekey(ino)]].directory ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) → (abs-dirs(fs, ri) \ abs-keys(orphans(fs, ri)))[ino] = mkdir (fs[(ri ⊖ orphans(fs, ri))[inodekey(ino)]].size, fs[(ri ⊖ orphans(fs, ri))[inodekey(ino)]].meta, fs[(ri ⊖ orphans(fs, ri))[inodekey(ino)]].nlink, fs[(ri ⊖ orphans(fs, ri))[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri ⊖ orphans(fs, ri))))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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