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Proof step 9 from proof abs-dirs-orphans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ (abs-dirs(fs, ri) \ abs-keys(orphans(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))), fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ 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)