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Proof step 19 from proof ri-closed-drop (previous step)

ri[inodekey(fs[ri[key]].key.ino)] ∈ as, key ∈ ri, ri[key] ∈ fs, fs[ri[key]].dentry? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].key.ino) ∈ ro ∧ fs[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 ∧ ¬ fs[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ # fs[ri[key]].data = VFS_PAGE_SIZE, ∀ adr. ¬ adr ∈ range ri ∩ as ⊦ # as = 0, as = ∅, ( 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)

User applied rule all left

And obtained the following new goals

Proof step 20:
ri[key] ∈ fs, key ∈ ri, ri[inodekey(fs[ri[key]].key.ino)] ∈ as, fs[ri[key]].data? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ # fs[ri[key]].data = VFS_PAGE_SIZE, fs[ri[key]].dentry? → inodekey(fs[ri[key]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].key.ino) ∈ ro ∧ fs[ri[inodekey(fs[ri[key]].key.ino)]].directory ∧ inodekey(fs[ri[key]].ino) ∈ ri ∧ ¬ inodekey(fs[ri[key]].ino) ∈ ro ⊦ # as = 0, as = ∅, ri[inodekey(fs[ri[key]].key.ino)] ∈ range ri ∩ as, ( 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)

Rule argument

pos: left 6 terms: ri[inodekey(fs[ri[key]].key.ino)] abort: F discard: T computed: F

Additional information

Used terms: ri[inodekey(fs[ri[key]].key.ino)]