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Proof step 15 from proof abs-dirs-orphans (previous step)

fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ 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 closed the goal!

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)% ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ ¬ dentrykey(m, str).inode?; (s) Used formulas: dentrykey(ino, str) ∈ orphans(fs, ri)