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Proof step 4 from proof datalkeys-drop-orphans (previous step)

ro.inodes? ⊦ key ∈ ro, ∀ key0. key0 ∈ datakeys(key, n, ri ⊖ ro) ↔ key0 ∈ datakeys(key, n, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
key0.ino = key.ino, key0.data?, key.inode?, ro.inodes?, n ≤ key0.part * VFS_PAGE_SIZE ⊦ key0 ∈ ri ⊖ ro ↔ key0 ∈ ri, key ∈ ro

Rule argument

Additional information

Used simplifier rules: ⊦ 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)