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Proof step 3 from proof abs-dirs-del-orphans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
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))))

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)%⊦ inodekey(ino) ∈ ri → (inodekey(ino) ∈ ri ⊖ ro ↔ ¬ inodekey(ino) ∈ ro); (s)