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Proof step 16 from proof replay-orphans-trunc (previous step)

key ∈ ro, datakey(m, m0) ∈ ri, ¬ key.inode? ∨ m ≠ key.ino ∨ ¬ n ≤ m0 * VFS_PAGE_SIZE ⊦ # ro = 0, (ri \ datakeys(key, n, ri))[datakey(m, m0)] = ri[datakey(m, m0)], ro = ∅, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

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] → [datakey(m, m0), datakeys(key, n, ri), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s)%⊦ 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)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s) Used terms: datakey(m, m0), datakeys(key, n, ri), ri