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Proof step 42 from proof ri-closed-gc-one (previous step)

ri[key, adr][inodekey(fs[ri[key0]].key.ino)] = adr, key ∈ ri, key0 ∈ ri, ri[key0] ∈ fs, fs[ri[key0]].dentry? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key0]].key.ino) ∈ ro ∧ fs[ri[inodekey(fs[ri[key0]].key.ino)]].directory ∧ inodekey(fs[ri[key0]].ino) ∈ ri ∧ ¬ inodekey(fs[ri[key0]].ino) ∈ ro, fs[ri[key0]].data? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[key0]].key.ino)]].directory ∧ # fs[ri[key0]].data = VFS_PAGE_SIZE, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ inodekey(fs[ri[key0]].key.ino) = key, key0 = key, adr ∈ fs, ( fs[ri[key0]].dentry? → inodekey(fs[ri[key0]].key.ino) ∈ ri[key, adr] ∧ ¬ inodekey(fs[ri[key0]].key.ino) ∈ ro ∧ fs[ri[key]].directory ∧ inodekey(fs[ri[key0]].ino) ∈ ri[key, adr] ∧ ¬ inodekey(fs[ri[key0]].ino) ∈ ro) ∧ (fs[ri[key0]].data? → inodekey(fs[ri[key0]].key.ino) ∈ ri[key, adr] ∧ ¬ fs[ri[key]].directory ∧ # fs[ri[key0]].data = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
key ∈ ri, key0 ∈ ri, ri[key0] ∈ fs, fs[ri[key0]].dentry? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key0]].key.ino) ∈ ro ∧ (∅)[ri[inodekey(fs[ri[key0]].key.ino)]].directory ∧ inodekey(fs[ri[key0]].ino) ∈ ri ∧ ¬ inodekey(fs[ri[key0]].ino) ∈ ro, fs[ri[key0]].data? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ (∅)[ri[inodekey(fs[ri[key0]].key.ino)]].directory ∧ # fs[ri[key0]].data = VFS_PAGE_SIZE, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ inodekey(fs[ri[key0]].key.ino) = key, key0 = key, ri[inodekey(fs[ri[key0]].key.ino)] ∈ fs, ( fs[ri[key0]].dentry? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ inodekey(fs[ri[key0]].key.ino) ∈ ro ∧ fs[ri[key]].directory ∧ inodekey(fs[ri[key0]].ino) ∈ ri[key, ri[inodekey(fs[ri[key0]].key.ino)]] ∧ ¬ inodekey(fs[ri[key0]].ino) ∈ ro) ∧ (fs[ri[key0]].data? → inodekey(fs[ri[key0]].key.ino) ∈ ri ∧ ¬ fs[ri[key]].directory ∧ # fs[ri[key0]].data = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)