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Proof step 11 from proof abs-dirs-deldatakeys-2 (previous step)

fs[ri[inodekey(ino)]].directory, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri ⊦ fs[(ri \ datakeys(key, n, ri))[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino, str)]].ino

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: dentrykey(ino, str) ∈ datakeys(key, n, ri)

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)% ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ dentrykey(m, str).data?; (s) Used formulas: dentrykey(ino, str) ∈ datakeys(key, n, ri)