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Proof step 13 from proof abs-dirs-orphans (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 14:
fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri \ orphans(fs, ri), fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, (dentrykey(ino, str) ∈ ri \ orphans(fs, ri) → dentrykey(ino, str) ∈ ri) ∧ (dentrykey(ino, str) ∈ ri \ orphans(fs, ri) → fs[(ri \ orphans(fs, ri))[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino, str)]].ino)

Rule argument

fma: dentrykey(ino, str) ∈ ri \ orphans(fs, ri)

Additional information

Used formulas: dentrykey(ino, str) ∈ ri \ orphans(fs, ri)