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Proof step 25 from proof replay-one-update (previous step)

fs[ri[datakey(ino, ino0)]].key = datakey(ino, ino0), fs[ri[datakey(ino, ino0)]].data?, ro.inodes?, orphans-cons(fs, ri, ro), ri-closed(ri, fs, ro), datakey(ino, ino0) ∈ ri, ri[datakey(ino, ino0)] ∈ fs, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ replay-one(adr, fs[ri[datakey(ino, ino0)]], ri ⊖ ro) = ri[datakey(ino, ino0), adr] ⊖ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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[datakey(ino, ino0)]], key0, buf]

Additional information

Used simplifier rules: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)); (elim) Used terms: fs[ri[datakey(ino, ino0)]], key0, buf