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Proof step 16 from proof ri-closed-gc-one (previous step)

key ∈ ri, ri[key] ∈ fs, fs[ri[key]].dentry? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].key.ino) ∈ ro ∧ (∅)[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ inodekey(fs[ri[key]].ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].ino) ∈ ro, fs[ri[key]].data? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ (∅)[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ # fs[ri[key]].data = VFS_PAGE_SIZE, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ inodekey(fs[ri[key]].key.ino) = key, ri[inodekey(fs[ri[key]].key.ino)] ∈ fs, ( fs[ri[key]].dentry? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].key.ino) ∈ ro ∧ fs[ri[key]].directory ∧ inodekey(fs[ri[key]].ino) ∈ ri[key, ri[inodekey(fs[ri[key]].key.ino)]] ∧ ¬ inodekey(fs[ri[key]].ino) ∈ ro) ∧ (fs[ri[key]].data? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ fs[ri[key]].directory ∧ # fs[ri[key]].data = VFS_PAGE_SIZE)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

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