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Proof step 18 from proof ri-closed-gc-one (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
fs[ri[key]] = dentrynode(key0, m), fs[ri[key]].dentry?, (∅)[ri[inodekey(key0.ino)]].directory, inodekey(m) ∈ ri[key, ri[inodekey(key0.ino)]], key ∈ ri, ri[key] ∈ fs, inodekey(key0.ino) ∈ ri, inodekey(m) ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ inodekey(key0.ino) = key, fs[ri[key]].data?, fs[ri[key]].directory, ri[inodekey(key0.ino)] ∈ fs, inodekey(m) ∈ ro, inodekey(key0.ino) ∈ ro

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[key]], key0, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[key]], key0, m