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Proof step 13 from proof abs-files-del-orphans (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 14:
inodekey(ino) ∈ ri, datakey(ino, n) ∈ ri, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, (datakey(ino, n) ∈ ri ⊖ orphans(fs, ri) ↔ datakey(ino, n) ∈ ri) ∧ (datakey(ino, n) ∈ ri ⊖ orphans(fs, ri) → fs[(ri ⊖ orphans(fs, ri))[datakey(ino, n)]].data = fs[ri[datakey(ino, n)]].data)

Rule argument

fma: datakey(ino, n) ∈ ri

Additional information

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