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Proof step 10 from proof abs-dirs-deldatakeys-2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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