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Proof step 22 from proof replay-one-update (previous step)

fs[ri[inodekey(ino)]] = inodenode(inodekey(ino), md, true, 0, m0, m1), ro.inodes?, ri-closed(ri, fs, ro), inodekey(ino) ∈ ro, inodekey(ino) ∈ ri, ri[inodekey(ino)] ∈ fs, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ # ro = 0, (ri ⊖ ro) -- inodekey(ino) = ri ⊖ ro, ino = 0, ino = ROOT_INO, ro = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: node-index name: notin-del-notin seq: ⊦ ¬ key ∈ ri → ri -- key = ri subst: [key, ri] → [inodekey(ino), ri ⊖ ro] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(ino) ∈ ri → (inodekey(ino) ∈ ri ⊖ ro ↔ ¬ inodekey(ino) ∈ ro); (s) Used terms: inodekey(ino), ri ⊖ ro