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Proof step 23 from proof ri-closed-drop (previous step)

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 = ∅, ∃ key0. key0 ∈ ri ∧ ri[key0] = ri[inodekey(fs[ri[key]].key.ino)], ( 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 exists right

And closed the goal!

Rule argument

pos: right 3 terms: inodekey(fs[ri[key]].key.ino) abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s) Used terms: inodekey(fs[ri[key]].key.ino)