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Proof step 16 from proof replayone-keep-adr (previous step)

key0 ∈ ri, ¬ key0.data? ∨ ¬ key.inode? ∨ key0.ino ≠ key.ino ∨ ¬ ino ≤ key0.part * VFS_PAGE_SIZE ⊦ (ri \ datakeys(key, ino, ri))[key0] = adr, (ri \ datakeys(key, ino, ri))[key0] ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Diff-get seq: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key] subst: [key, ks, ri] → [key0, datakeys(key, ino, ri), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)%key ∈ ri ⊦ ri[key] ∈ ri; (s)% ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s) Used terms: key0, datakeys(key, ino, ri), ri