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Proof step 29 from proof replay-orphans-trunc (previous step)

key ∈ ro ⊦ # ro = 0, datakey(m, m0) ∈ ri \ datakeys(key, n, ri) ↔ datakey(m, m0) ∈ ri, ro = ∅, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks

Rule argument

spec: store+set, inst: node-index name: Diff-ext seq: ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks subst: [ks, ri, key] → [datakeys(key, n, ri), ri, datakey(m, m0)] 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)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ key.inode? → inodekey(key.ino) = key; (s) Used terms: datakeys(key, n, ri), ri, datakey(m, m0)