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Proof step 2 from proof abs-dirs-del-orphans (previous step)

⊦ ( 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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 3:
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))))

Rule argument

fma: inodekey(ino) ∈ ri

Additional information

Used simplifier rules: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws) Used formulas: inodekey(ino) ∈ ri