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Proof step 49 from proof ri-closed-gc-one (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
# buf = VFS_PAGE_SIZE, fs[ri[key0]] = datanode(key1, buf), fs[ri[key0]].data?, fs[ri[key]].directory, inodekey(key1.ino) ∈ ri, ri[key0] ∈ fs, key0 ∈ ri, key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ inodekey(key1.ino) = key, key0 = key, fs[ri[key0]].dentry?, (∅)[ri[inodekey(key1.ino)]].directory, ri[inodekey(key1.ino)] ∈ fs

Rule argument

spec: node name: elim-05 seq: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)) subst: [nd, key, buf] → [fs[ri[key0]], key1, buf]

Additional information

Used simplifier rules: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)); (elim) Used terms: fs[ri[key0]], key1, buf