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Proof step 33 from proof replay-one-update (previous step)

# buf = VFS_PAGE_SIZE, fs[ri[datakey(ino, ino0)]] = datanode(datakey(ino, ino0), buf), ro.inodes?, orphans-cons(fs, ri, ro), ri[datakey(ino, ino0)] ∈ fs, datakey(ino, ino0) ∈ ri, inodekey(ino) ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ (ri ⊖ ro)[datakey(ino, ino0), adr] = ri[datakey(ino, ino0), adr] ⊖ ro, fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: replay-orphans-data seq: ⊦ ¬ datakey(ino, n) ∈ ro ∧ ¬ inodekey(ino) ∈ ro → (ri ⊖ ro)[datakey(ino, n), adr] = ri[datakey(ino, n), adr] ⊖ ro subst: [adr, n, ino, ro, ri] → [adr, ino0, ino, ro, ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s) Used terms: adr, ino0, ino, ro, ri